Linear extensions, linear averagings, and their applications to linear topological classification of spaces of continuous functions

Pełczyński, A.

Książka - szczegóły

Tytuł książki

Linear extensions, linear averagings, and their applications to linear topological classification of spaces of continuous functions

Autorzy

A. Pełczyński

Seria

Rozprawy Matematyczne tom/nr w serii: 58 wydano: 1968

Zawartość

Pełne teksty:

Pobierz

Warianty tytułu

Abstrakty

EN

CONTENTS
Introduction................................................................................................................................................. 5
Preliminaries.............................................................................................................................................. 9
§ 1. Regular operators and their products............................................................................................ 11
§ 2. Exaves. Extension and averaging operators................................................................................. 15
§ 3. Linear multiplicative exaves and retractions. Localization principle......................................... 21
§ 4. Integral representations and compositions of linear exaves.................................................... 22
§ 5. Milutin spaces..................................................................................................................................... 27
§ 6. Dugundji spaces................................................................................................................................ 34
§ 7. Exaves and topological groups....................................................................................................... 37
§ 8. Application to linear topological classification of spaces of continuous functions............... 40
§ 9. Linear averaging operators and projections onto spaces of continuous functions.............. 47
Notes and Remarks.................................................................................................................................. 59
Appendix: Category-theoretical approach............................................................................................. 75
Bibliography................................................................................................................................................ 80

Słowa kluczowe

Tematy

Wydawca

Instytut Matematyczny Polskiej Akademii Nauk

Miejsce publikacji

Warszawa

Copyright

Seria

Rozprawy Matematyczne tom/nr w serii: 58

Liczba stron

89

Liczba rozdzia³ów

Opis fizyczny

Rozprawy Matematyczne, Tom LVIII

Daty

wydano

1968

Twórcy

autor

A. Pełczyński

Bibliografia

[1] R. Adams, N. Aronszajn and K. Smith, Theory of Bessel potentials. Part II, Ann, Inst. Fourier 17.2 (1967), 1-135.
[2] P. S. Alexandroff, On the theory of topological spaces, Dokl. Akad. Nauk SSSR 2 (1936), 51-54.
[3] P. S. Alexandroff and V. I. Ponomarev, On dyadic bicompacta, Fund. Math. 50 (1962), 419-429 (Russian).
[4] D. Amir, Continuous function spaces with the bounded extension property, Bull. Res. Counc. of Israel 10 F (1962), 133-138.
[5] D. Amir, Projections onto continuous function spaces, Proc. Amer. Math. Soc. 15 (1964), 396-402.
[6] D. Amir, On projections and simultaneous extensions, Israel J. Math. 2 (1964), 245-248.
[7] D. Amir, On isomorphism of continuous function spaces, Israel J. Math. 3 (1965). 205-210.
[8] R. Arens, Extensions of functions on fully normal spaces, Pacific J. Math. 2 (1952), 11-22.
[9] R. Arens, Projections on continuous function spaces, Duke Math. Journal 32 (1965), 469-478.
[10] N. Aronszajn, Potentiels bessélien, Annales de l'lnstitut Fourier 15 (1965), 43-58.
[11] N. Aronszajn and P. Panitchpakdi, Extension of uniformly continuous transformations and hyperconvex metric spaces, Pacific J. Math. 6 (1956), 405-439.
[12] S. Banach, Théorie des opérations linéaires, Warszawa 1932.
[13] S. Banach, Theory of functions of real variables, Warszawa 1951 (Polish).
[14] C. Bessaga, On topological classification of complete linear metric spaces, Fund. Math. 56 (1965), 251-288.
[15] C. Bessaga and A. Pełczyński, Spaces of continuous functions (IV) (On isomorphic classification of spaces of continuous functions), Studia Math. 19 (1960), 53-62.
[16] C. Bessaga and A. Pełczyński, Some remarks on homeomorphism of Banach spaces, Bull. Acad. Polon. Sci. ser. sci. math., astr. et phys. 8 (1960), 757-761.
[17] C. Bessaga and A. Pełczyński, Some remarks on homeomorphisms of F-spaces, ibidem 10 (1962), 265-270.
[18] R. H. Bing, Metrization of topological spaces, Canadian J. Math. 3 (1951), 175-186.
[19] R. H. Bing, Extending a metric, Duke Math. J. 14 (1947), 511-519.
[20] G. Birkhoff, Moyennes de fonctions bornées, Algèbre et Théorie des Numbres, Colloques International du Centre Nation, de la Rech. Scient. N° 24 (1950), 143-153.
[21] G. Birkhoff, Lattices in applied mathematics, Proceedings of Symposia in Pure Mathematics, volume II (1961), Lattice Theory, 155-184.
[22] E. Bishop, A general Rudin-Carleson theorem, Proc. Amer. Math. Soc. 13 (1962), 140-143.
[23] F. Bohnenblust, Convex regions and projections in Minkowski spaces, Ann. of Math. 39 (1938), 301-308.
[24] M. Bockstein, Un théorème de séparabilité pour les produits topologiques, Fund. Math. 35 (1948), 242-246.
[25] F. F. Bonsall, J. Lindenstrauss and R. R. Phelps, Extreme positive operators on algebras of functions, Math. Scand. 18 (1966), 161-182.
[26] A. Borel, Sections locales de certains espaces fibrés, Comptes Rendus de l'Academie des Sciences (Paris), 230 (1950), 1246-1248.
[27] C. J. R. Borges, On stratifiable spaces, Pacific J. Math. 17 (1966), 1-16.
[28] K. Borsuk, Über Isomorphie der Funktionalräume, Bull. Int. Acad. Pol. Sci. 1933, 1-10.
[29] K. Borsuk, Sur les rétractes, Fund. Math. 17 (1931), 152-170.
[30] K. Borsuk, Über eine Klasse von lokal zusammenhängenden Räumen, ibid. 19 (1932), 235-242.
[31] K. Borsuk, Theory of retracts, Monogr. Mat. 44, Warszawa 1967.
[32] N. Bourbaki, Algèbre, Chapitre III, Elements de Mathématique, Hermann 1948.
[33] N. Bourbaki, Topologie générale, Chap. 10, Éléments de Mathématique, Hermann, Paris 1949.
[34] On the structure of averaging operators, J. Math. Analys. and Appl. 5 (1962), 347-377.
[35] B. Brainerd, Averaging operators on the ring of continuous functions on compact space, Australian J. Math. 4 (1964), 293-298.
[36] L. de Branges, The Stone-Weierstrass theorem, Proc. Amer. Math. Soc. 10 (1959); 822-824
[37] H. B. Brinkmann und E. Puppe, Kategorien und Funktoren, Berlin-Heidelberg-New York 1966.
[38] L. E. Brouwer, Invarianz des n-dimensionalen Gebiets, Math. Ann. 71 (1912), 305-313.
[39] L. E. Brouwer, Über die Erweiterung des Definitionsbereichs einer stetigen Funktion, ibidem 79 (1918), 209-211.
[40] A. P. Calderón, Lebesgue spaces of differentiable functions and distributions, Proc. Symp. Pure Math. vol. 4 (1961) Partial differential equations, 33-49.
[41] C. Carathéodory, Vorlesungen über reelle Funktionen, first edition, Leipzig-Berlin 1918.
[42] C. Carathéodory, Vorlesungen über reelle Funktionen, second edition, Leipzig 1927.
[43] L. Carleson, Representations of continuous functions, Math. Zeit. 66 (1957), 447-451.
[44] J. Cipszer and L. Geher, Extension of functions satisfying a Lipschitz condition, Acta Math. Acad. Sci. Hungar. 6 (1955), 213-220.
[45] H. B. Cohen, Injective envelopes of Banach spaces, Bull. Amer. Math. Soc. 70 (1964), 723-726.
[46] H. H. Corson, Normality in subsets of product spaces, American Journal of Mathematics 81 (1959), 785-796.
[47] H. H. Corson, The weak topology of a Banach space, Trans. Amer. Math. Soc. 101 (1961), 1-15.
[48] H. H. Corson and J. Lindenstrauss, On simultaneous extension of continuous functions. Bull. Amer. Math. Soc. 71 (1965), 542-545.
[49] H. H. Corson and J. Lindenstrauss, Continuous selections with non-metrizable range, Trans. Amer. Math. Soc. 121 (1966), 492-504.
[50] M. M. Day, Normed linear spaces, New York 1962.
[51] M. M. Day, Strict convexity and smoothness of normed spaces, Trans. Amer. Math. Soc. 78 (1955), 516-528.
[52] L. Danzer, B. Grünbaum and V. Klee, Helly's theorem and its relatives, Amer. Math. Soc., Proceedings of Symposia in Pure Mathematics 7, Convexity 1963, 101-180.
[53] C. Davis, Various averaging operations onto subalgebras, Illinois J. Math. 3 (1959), 538-553.
[54] D. W. Dean, Subspaces of C(H) which are direct factors of C (H), Proc. Amer. Math. Soc. 16 (1965), 237-242.
[55] D. W. Dean, Projections in certain continuous function spaces, Canadian J. Math. 14 (1962), 385-401.
[56] Ch. J. de la Vallée Poussin, Intégrales de Lebesgue, functions d'ensemble, classes de Baire, 1934, second édition.
[57] C. H. Dowker, On theorem of Hanner, Ark. Math. 2 (1952), 307-313.
[58] J. Dugundji, An extension of Tietze's theorem, Pacific J. Math. 1 (1951), 353-367.
[59] N. Dunford and J. T. Schwartz, Linear Operators I, New York 1958.
[60] B. Efimov, On dyadic spaces, Dokl. Akad. Nauk SSSR 151 (1963), 1021-1024 (Russian).
[61] B. Efimov, Matrizability and E-product of compact spaces, ibidem 152 (1963), 794-797 (Russian).
[62] B. Efimov, On weight structure of dyadic compacts, Vestnik Moscov. Univ. 2 (1964), 3-11 (Russian).
[63] B. Efimov and R. Engelking, Remarks on dyadic spaces, II, Colloquium Mathematicum 13 (1965), 181-197.
[64] S. Eilenberg, Extensions and classification of continuous mappings, Lectures in Topology, 57-100. Ann Arbor, Michigan 1941.
[65] S. Eilenberg and N. Steenrod, Foundations of algebraic topology, Princeton, Now Jersey 1952.
[66] R. Engelking, Cartesian products and dyadic spaces, Fund. Math. 57 (1965), 287-304.
[67] R. Engelking and A. Pełczyński, Remarks on dyadic spaces, Colloquium Mathematicum 11 (1963), 55-63.
[68] A. Esenin-Volpin, On connection between local and global weight of dyadic compacta, Dokl. Akad. Nauk SSSR 68 (1949), 441-444 (Russian).
[69] C. Foiaş and I. Singer, On bases in C([0, 1]) and $L^1([0, 1])$, Rev. Roumaine Math. Pures et Appl. 10 (1965), 931-960.
[70] T. W. Gamelin, Restrictions of subspaces of C(X), Trans. Amer. Math. Soc. 112 (1964), 278-286.
[71] L. Gillman and M. Jerison, Rings of Continuous Functions, New York 1960.
[72] A. M. Gleason, Projective topological spaces, Illinois J. Math. 2 (1958), 482-489.
[73] I. Glicksberg, Some uncomplemented function algebras, Trans. Amer. Math. Soc. Ill. (1964), 121-137.
[74] D. B. Goodner, Projections in normed linear spaces, Trans. Amer. Math. Soc. 69 (1950), 89-108.
[75] A. Grothendieck, Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc. 16 (1955).
[76] A. Grothendieck, Sur les applications linéaires faiblement campactes d'espaces du type C(K), Canadian J. Math. 5 (1953), 129-173.
[77] B. Grünbaum, Some applications of expansion constants, Pacific J. Math 10 (1960), 193-201.
[78] B. Grünbaum, Projections onto some function spaces, Proc. Amer. Math. Soc. 13 (1962), 316-324.
[79] O. Hanner, Retraction and extension of mappings of metric and non-metric spaces, Ark. Mat. 2 (1952), 315-360.
[80] O. Hanner, Solid spaces and absolute retracts, ibidem 1 (1951), 375-385.
[81] O. Hanner, Some theorems on absolute neighbourhood retracts, ibidem 1 (1951), 389-408.
[82] M. Hasumi, The extension, property of complex Banach spaces, Tôhoku Math. J. 10 (1958), 135-142.
[83] F. Hausdorff, Mengenlehre, Dover, New York 1944.
[84] F. Hausdorff, Über halbstetige Funktionen und deren verallgemeinerung, Math. Zeit. 5 (1919), 292-309.
[85] F. Hausdorff, Erweiterung einer stetigen. Abbildung, Fund. Math. 30 (1938), 40-47.
[86]. M. R. Hestenes, Extension of the range of a differentiable function, Duke Math. J. 8 (1941), 183-192.
[87] E. Hewitt, A note on O-dimensional compact groups, Fund. Math. 50 (1961), 95-97.
[88] E. Hewitt and K. A. Ross, Abstract harmonic analysis, Berling-Göttingen-Heidelberg 1963.
[89] S. T. Hu, Homotopy theory, New York 1959.
[90] S. T. Hu, Theory of retracts, Detroit 1965.
[91] A. Hulanicki, On the topological structure of 0-dimensional topological groups Fund. Math, 46 (1959), 317-320.
[92] A. Hulanicki, On locally compact topological groups of power of continuum, ibidem 44 (1957), 156-158.
[93] A. Hulanicki, On cardinal numbers related with locally compact groups, Bull. Acad. Polon. Sci., Ser. sci. math., astr. et phys. 6 (1958), 67-70.
[94] W. Hurewicz and H. Wallman, Dimension theory, Princeton University Press 1941.
[95] A. Ionescu-Tulcea, On the lifting property V, Ann. Math. Statist. 36 (1965), 819-828.
[96] C. Ionescu-Tulcea, On the lifting property and disintegration of measures, Bull. Amer. Math. Soc. 71 (1960), 829-842.
[97] J. R. Isbell, Uniform spaces, American Math. Society, Providence 1964.
[98] J. R. Isbell and Z. Semadeni, Projection constants and spaces of continuous functions, Trans. Amer. Math. Soc. 107 (1963). 38-48.
[99] L. Ivanovskiǐ, On a hypothesis of P. S. Alexandroff, Dokl. Akad. Nauk SSSR 123 (1958), 785-786 (Russian).
[100] B. F. Jones, On the first countability axiom for locally compact Hausdorff spaces, Colloq. Math. 7 (1959), 33-34.
[101] M. I. Kadec and B. Ya. Levin, On a solution of Banach problem concerning topological equivalence of spaces of continuous functions, Trudy Semin. Funct. Anal. Voronesh 3-4 (1960), 20-25 (Russian).
[102] J. Kampé de Férriet, L'état actuel du problène de la turbulence I, La science Aéronautique 3 (1934), 9-34.
[103] J. Kampé de Férriet, L'état actuel du problème de la turbulence II, ibidem 4 (1935), 12-52.
[104] S. Kakutani, Simultaneous extension of continuous functions considered as positive defined linear operation, Jap. J. Math. 17 (1940), 1-4.
[105] J. L. Kelley, Averaging operators on $C_∞(X)$, Illinois J. Math. 2 (1958), 214-223.
[106] J. L. Kelley, General topology, Princeton, New Jersey, 1955.
[107] J. L. Kelley, Banach spaces with extension property, Trans. Amer. Math. Soc. 72 (1952), 323-326.
[108] M. D. Kirszbraun, Über die zusammenziehende und Lipschitzschen Transformationen, Fund. Math. 22 (1934), 77-108.
[109] V. L. Klee, Convex bodies and periodic homeomorphism in Hilbert space, Trans. Amer. Math. Soc. 74 (1953), 10-43.
[110] B. R. Kripke and R. B. Holmes, Approximation of bounded functions by continuous functions, Bull. Amer. Math. Soc. 71 (1965), 896-897. '
[111] C. Kuratowski, Topologie I, 4th edition, Warszawa 1958.
[112] C. Kuratowski, Topologie II, 4th edition, Warszawa 1961.
[113] C. Kuratowski, Remarque sur les transformations continues des espaces métriques, Fund. Math. 30 (1938), 48-49.
[114] V. Kuzminov, On a hypothesis of P. S. Aleksandroff in the theory of topological groups, Dokl. Akad. Nauk SSSR 125 (1959), 727-729 (Russian).
[115] H. Lebesgue, Sur le problème de Dirichlet, Rendiconti di Palermo 24 (1907), 371-402.
[116] Ł. Lichtenstein, Eine elementare Bemerkung zur reellen Analysis, Math. Z. 30 (1929), 794-795.
[117] J. Lindenstrauss, Extension of compact operators, Mem. Amer. Math. Soc. No 48 (1964).
[118] J. Lindenstrauss, On non-linear projections in Banach spaces, Michigan Math. Journal 11 (1964), 268-287.
[119] S. P. Lloyd, On certain projections in spaces of continuous functions, Pacific J. Math. 13 (1963), 171-175.
[120] S. P. Lloyd, On extreme averaging operators, Proc. Amer. Math. Soc. 14 (1963), 305-310.
[121] E. Marczewski (E. Szpilrajn), Remarque sur les produits cartésiens d'espaces topologiques, Dokl. Akad. Nauk SSSR 31 (1941), 525-528.
[122] S. Mardésić and P. Papić, Continuous images of ordered compacta, the Suslin property and dyadic compacta, Glasnik Mat.-Fiz. i Astr. 17 (1962), 3-25.
[123] S. Mazurkiewicz et W. Sierpiński, Contributions à la topologie des ensembles dénombrables, Fund. Math. 1 (1920), 17-27.
[124] E. J. McShane, Extension of range of functions, Bull. Amer. Math. Soc. 40 (1934), 837-842.
[125] E. J. McShane, Necessary conditions in generalized-curve problems of the calculus of variations Duke Math. J. 7 (1940), 25-27.
[126] R. D. McWilliams, On projections of separable subspaces of (m) onto (c), Proc. Amer. Math. Soc. 10 (1959), 872-876.
[127] E. Michael, Some extension theorems for continuous functions, Pacific J. Math. 3 (1953), 789-806.
[128] E. Michael, A linear mapping between function spaces, Proc. Amer. Math. Soc. 15 (1964), 407-409.
[129] E. Michael, Three mapping theorems, Proc. Amer. Math. Soc. 15 (1964), 410-415.
[130] E. Michael, Convex structures and continuous selections, Canadian J. Math. 11 (1959), 556-575.
[131] E. Michael, Continuous selections I, Annals of Math. 63 (1956), 361-382.
[132] E. Michael, Continuous selections II, ibidem 64 (1956), 562-580.
[133] E. Michael, Continuous selections III, idibem 65 (1957), 375-390.
[134] E. Michael and A. Pełczyński, A linear extension theorem, Illinois J. Math. 11 (1967), 563-579.
[135] E. J. Mickle, On the extension of a transformation, Bull. Amer. Math. Soc. 55 (1949), 160-164.
[136] A. A. Milutin, On spaces of continuous functions, Dissertation, Moscow State University, 1952 (Russian).
[137] A. A. Milutin, Isomorphism of spaces of continuous functions on compacta of power continuum, Tieoria Funct., Funct. Anal, i Pril. (Kharkov) 2 (1966), 150-156 (Russian).
[138] B. Mitchell, Theory of categories, New York-London 1965.
[139] B. S. Mitjagin, Approximative dimension and bases in nuclear spaces, Usp. Mat. Nauk, 16 J6 4 (1961), 63-132 (Russian).
[140] D. Montgomery and L. Zippin, Topological transformation groups, New York 1955.
[141] P. S. Mostert, Sections in principal fibre spaces, Duke Math. J. 23 (1956), 57-72.
[142] S. T. Chen Moy, Characterizations of conditional expectation as a transformation on function spaces, Pacific J. Math 4 (1954), 47-63.
[143] L. Nachbin, Some problems in extending and lifting continuous linear transformations, Proc. Internat. Sympos. on Linear Spaces, Jerusalem (1961), 340-350.
[144] J. Nagata, Modern dimension theory, Amsterdam 1965.
[145] C. Olech, Approximation of set-valued functions by continuous functions, to appear in Colloq. Math. 19 (1968).
[146] Z. Ogrodzka, On simultaneous extension of infinitely differentiable functions. Studia Mathematica 28 (1967), 193-207.
[147] A. Pełczyński, On simultaneous extension of continuous functions, Studia Mathematics 24 (1964), 285-304.
[148] A. Pełczyński, Supplement to my paper on simultaneous extension of continuous functions. Studia Mathematica 25 (1964), 157-161.
[149] A. Pełczyński, Projections in certain Banach spaces, Studia Mathematica 19 (1900), 209-228.
[150] A. Pełczyński, On the isomorphism of spaces m and M, Bull. Acad, Polon. Sci., ser. sci. math., astr. et phys. 6 (1958), 695-696.
[151] A. Pełczyński, A generalisation of Stone's theorem on approximation. Bull. Acad. Polon. Sci., Cl. III. 5 (1957). 105-107.
[152] A. Pełczyński and Z. Semadeni, Spaces of continuous functions (III), Studia Mathematics 18 (1959), 211-222.
[153] A. Pełczyński and V. N. Sudakov, Remark on non-complemented subspaces of the space m(S), Colloq. Math. 19 (1962), 85-88.
[154] R. R. Phelps, Extreme positive operators and homomorphisms, Trans. Amer. Math. Soc. 108 (1963), 265-274.
[155] V. I. Ponomarev, On dyadic spaces, Fund. Math. 52 (1963), 351-354 (Russian).
[156] L. S. Pontryagin, Continuous groups, 2nd edition, 1954 (Russian). German translation: Topologische Gruppen, I, II, Leipzig 1951 and 1958.
[157] O. Reynolds, On the dynamical theory of incompressible viscous fluids and the determination of the criterion. Philos. Trans. Roy. Soc., Ser. A 186 (1894), 123-164.
[158] H. P. Rosenthal, Projections onto translation invariant subspaces of $L^p(G)$, Mem. Amer. Math. Soc. 63 (1966).
[159] K. A. Ross and A. H. Stone, Product of separable spaces, Amer. Math. Monthly 71 (1964), 398-403.
[160] C. C. Rota, On the representation of averaging operators, Rendiconti del Seminaro Matematico della Universita di Padova 30 (1960), 52-64.
[161] C. C. Rota, Reynolds operators, Proceedings of Symposia Applied Mathematics volume 16. Stochastic processes in mathematical physics and engineering, Amer. Math. Soc. 1964, 70-83.
[162] W. Rudin, Projections on invariant subspaces, Proc. Amer. Math. Soc. 13 (1962), 429-432.
[163] W. Rudin, Boundary values of continuous analytic functions. Proc. Amer. Math. Soc. 7 (1956), 808-811.
[164] N. Šanin, On the product of topological spaces, Trudy Mat. Inst. Steklova 24 (1948) (Russian).
[165] R. T. Seeley, Extension of $C^∞$ functions defined in a half-space, Proc. Amer. Math. Soc. 15 (1964), 625-626.
[166] Z. Semadeni, Isomorphic properties of Banach spaces of continuous functions, Studia Mathematica, Seria specjalna (1963), 93-108.
[167] Z. Semadeni, Simultaneous extensions and projections in spaces of continuous functions, Lecture Notes at Aarhus University, May 1965.
[168] J. P. Serre, Trivialité des espaces fibrés. Applications, Comptes Rendus de l'Academie des Sciences (Paris) 230 (1950), 916-918.
[169] E. G. Sklyarenko, On the topological structure of factor spaces of locally bicompact groups, Dokl. Akad. Nauk SSSR 145 (1962), 1004-1007 (Russian).
[170] A. Sobczyk, Projection of the space (m) on its subspace ($c_o$), Bull. Amer. Math. Soc. 47 (1941), 938-947.
[171] N. E. Steenrod, The topology of fibre bundles, Princeton 1951.
[172] H. Tietze, Über Funktionen, die auf einer abgeschlossenen Menge stetig sind, Journal f. Math. 145 (1915), 9-14.
[173] P. S. Urysohn, Über die Mächtigkeit der zusammenhängenden Mengen, Mathematische Annalen 94 (1925), 262-295.
[174] F. A. Valentine, On the extension of a vector function so as to preserve a Lipschitz condition, Bull. Amer. Math. Soc. 49 (1943), 100-108.
[175] F. A. Valentine, Contractions in non-Euclidean spaces, Bull. Amer. Math. Soc. 50 (1944), 710-713.
[176] F. A. Valentine, A Lipschitz condition preserving extension for a vector function, Amer. J. Math. 67 (1945), 83-93.
[177] H. Whitney, Analytic extensions of differentiable functions defined in closed sets, Trans. Amer. Math. Soc. 36 (1934), 63-89.
[178] H. Whitney, Differentiable functions defined in closed sets, Trans. Amer. Math. Soc. 36 (1934), 369-387.
[179] A. Weil, L'intégration dans les groupes topologiques et ses applications, Hermanet Cie., Act. Sci. et Jud. 869-1145, deuxième edition, Paris 1953.
[180] F. B. Wright, Generalized means, Trans. Amer. Math. Soc. 98 (1961), 187-203.
[181] H. Yoshizawa, On simultaneous extension of continuous functions, Proc. Imp. Acad. Tokyo, 20 (1944), 653-654.

Języki publikacji

EN

Uwagi

Identyfikator YADDA

bwmeta1.element.desklight-a781ce7b-ef0c-4168-98ad-7c86ff63a306

Identyfikatory

Kolekcja

DML-PL

Zawartość książki

rozwiń roczniki

Książka - szczegóły

Linear extensions, linear averagings, and their applications to linear topological classification of spaces of continuous functions

Autorzy

Seria

Zawartość

Warianty tytułu

Abstrakty

Słowa kluczowe

Tematy

Wydawca

Miejsce publikacji

Copyright

Seria

Liczba stron

Liczba rozdzia³ów

Opis fizyczny

Daty

Twórcy

Bibliografia

Języki publikacji

Uwagi

Identyfikator YADDA

Identyfikatory

Kolekcja