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Zawartość
Pełne teksty:
Warianty tytułu
Abstrakty
CONTENTS
INTRODUCTION........................................................................................................................................ 3
I. PROJECTIVITY AND INJECTIVITY IN ABSTRACT BICATEGORIES.............................................. 7
§ 1. Categories and bicategories........................................................................................................... 7
§ 2. Arrow notation and the duality principle......................................................................................... 10
§ 3. Singletons........................................................................................................................................... 11
§ 4. Projective and injective objects....................................................................................................... 12
§ 5. Separators and generators............................................................................................................. 13
§ 6. Free and direct objects..................................................................................................................... 10
II. SOME SPECIAL BICATEGORIES....................................................................................................... 10
§ 7. Table of examples............................................................................................................................. 10
§ 8. Topological spaces........................................................................................................................... 10
§ 9. Groups. Abelian groups. Modules over a ring.............................................................................. 25
§ 10. Locally compact abelian groups.................................................................................................. 28
§ 11. Boolean algebras. Compact spaces.......................................................................................... 29
§ 12. Banach spaces. Linear topological spaces.............................................................................. 31
§ 13. Two-norm spaces and linear spaces with mixed topology.................................................... 33
APPENDIX.................................................................................................................................................. 38
§ 14. Remarks on subobject and injections....................................................................................... 38
§ 16. Tricategories................................................................................................................................... 41
REFERENCES.......................................................................................................................................... 44
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne
tom/nr w serii:
35
Liczba stron
47
Liczba rozdzia³ów
Opis fizyczny
Rozprawy Matematyczne, Tom XXXV
Daty
wydano
1963
Twórcy
autor
- The Institute of Mathematics of the Polish Academy of Sciences, The University of Washington, Seattle
Bibliografia
- A. Alexiewicz and Z. Semadeni, A generalization of two-norm spaces. Linear functionals, Bull. Acad. Polon. Sci., Sér. des sci. math., astr. et phys., 6 (1958), p.135-139.
- A. Alexiewicz and Z. Semadeni, Linear functionals on two-norm spaces, Studia Math. 17 (1958), p. 121-140.
- A. Alexiewicz and Z. Semadeni, The two-norm spaces and their conjugate spaces, Studia Math. 18 (1959), p. 275-283.
- A. Alexiewicz and Z. Semadeni, Some properties of two-norm spaces and a characterization of reflexivity of Banach spaces, Studia Math. 19 (1960), p. 115-132.
- D. Amir, Continuous functions spaces with the bounded extension property, Bull. Res. Council Israel. 10F (1962), p. 133-138.
- R. Baer, Abelian groups that are direct summands of every containing abelian group, Bull. Amer. Math. Soc. 46 (1940), p. 800-806.
- R. Baer, Absolute retracts in group theory, Bull. Amer. Math. Soc. 52 (1946), p. 501-506.
- S. Banach, Théorie des opérations linéaires, Warszawa 1932.
- S. Banach und S. Mazur, Zur Theorie der linearen Dimension, Studia Math. 4 (1933), p. 100-112.
- H. Bauer, Über die Fortsetzung positiver linearer Formen, Bayerische Akad. Wissensch. 1957, Sonderdruck 11, p. 177-190.
- E. Bishop and R. R. Phelps, A proof that every Banach space is sub-reflexive, Bull. Amer. Math. Soc. 67 (1961), p. 97-98.
- K. Borsuk, Sur les retractes, Fund. Math. 17 (1931), p. 152-170.
- N. Bourbaki, Espaces vectoriels topologiques, Actual. Sci. Ind. 1229 (1955).
- D. Buchsbaum, Exact categories and duality, Trans. Amer. Math. Soc. 80 (1955), p. 1-34.
- H. Cartan and S. Eilenberg, Homological Algebra, Princeton 1956.
- M. M. Day, Normed Linear Spaces, Erg. Math., 1958.
- J. Dieudonné, La dualité dans les espaces vectoriels topologiques, Ann. Sci. Ecole Norm. Sup. 59 (1942), p. 107-139.
- J. Dugundji, Absolute neighborhood retracts and local connectedness in arbitrary metric spaces, Compositio Math. 13 (1958), p. 229-246.
- S. Eilenberg and S. MacLane, General theory of natural equivalences, Trans. Amer. Math. Soc. 58 (1945), p. 231-294.
- L. Gillman and M. Jerison, Rings of continuous functions, New York 1959.
- A.M. Gleason, Projective topological spaces, Illinois J. Math. 2 (1958), p. 482-489.
- I. Glicksberg, Uniform boundedness for groups, Canadian J. Math. 14 (1962), p. 269-276.
- K. Gödel, The consistence of the axiom of choice and of the generalized continuum hypothesis with the axioms of set theory, Annals of Math. Studies 3, Princeton 1940.
- D. A. Goodner, Projections in normed linear spaces, Trans. Amer. Math. Soc. 69 (1950), p. 89-108.
- A. Grothendieck, Sur les applications linéaires faiblement continues d'espaces du type C(K), Canadian J. Math. 5 (1953), p. 129-173.
- A. Grothendieck, Une caractérization vectorielle métrique des espaces L¹, Canadian J. Math. 7 (1955), p. 552-561.
- A. Grothendieck, Sur quelques points d'algèbre homologique, Tôhoku Math. J. 9 (1957), p. 119-221.
- A. Grothendieck, Sur la completion du dual d'un espace vectoriel localement convexe, C. R. Paris 230 (1950), p. 605-606.
- A. Grothendieck, Produits tensoriels topologiques et espaces nucléaires, Memoirs Amer. Math. Soc. 16 (1955).
- M. Hall, The Theory of Groups, New York 1959.
- P. R. Halmos, Boolean Algebras (mimeographed), 1959.
- P. R. Halmos, Injective and projective Boolean algebras. Proc. Symp. Pure Math. 2 (1961), p. 114-122.
- A. Heller, Homological algebra in abelian categories, Ann. of Math. 68 (1958), p. 484-525.
- E. Hewitt and K. A. Ross, Abstract Harmonic Analysis, Berlin. 1963.
- J. R. Isbell, Some remarks concerning categories and subspaces, Canadian J. Math. 9 (1957), p. 563-577.
- J. R. Isbell, Algebras of uniformly continuous functions, Ann. of Math. 68 (1958), p. 96-125.
- J. R. Isbell, Natural sums and direct decompositions, Duke Math. J. 27 (1960), p. 507-512.
- J. R. Isbell, Adequate subcategories, Illinois J. Math. 4 (1960), p. 541-552.
- J. R. Isbell, Subobjects, adequacy, completeness and categories of algebras, Rozprawy Matemat. 38 (1964).
- J. R. Isbell, Uniform Spaces, in preparation.
- J. R. Isbell and Z. Semadeni, Projection constants and spaces of continuous functions, Trans. Amer. Math. Soc. 107 (1963), p. 38-48.
- J. P. Jans, Homological Algebra and Ming Theory (mimeographed), Oklahoma State University, 1961.
- J. L. Kelley, Banach spaces with the extension property, Trans. Amer. Math. Soc. 72 (1952), p. 323-326.
- J. L. Kelley, General Topology, New York 1955.
- S. Kaczmarz und H. Steinhaus, Theorie der Orthogonalreihen, Warszawa 1935.
- V.L. Klee, Some new results on smoothness and rotundity in normed linear spaces, Math. Annalen 139 (1959), p. 51-63.
- M. G. Krein, Про позитивнi адитивнi функцiонали в лiнiйних нормованих просторахз, Zapiski Nauk. Dosl. Inst. Mat. Mech. Kharkov 14 (1937), p. 227-237.
- C. Kuratowski, Topologie, I (second ed.) and II, Warszawa 1948 and 1950.
- A. G. Kurosh:, Theory of Groups (English translation), vol. 1 and 2, New York 1955 and 1956.
- A. G. Kurosh, A. H. Livshic and E.G. Shulgeifer, Foundations of the theory of categories, English translation in Russian Math. Surveys from Uspiekhy Mat. Nauk 15 (1960), (6), p. 1-46.
- S.MacLane, Duality for groups, Bull. Amer. Math. Soc. 50(1950), p. 485-516.
- S. Mazur and W. Orlicz, Sur les espaces métriques linéaires (II), Studia Math. 13 (1953), p. 137-179.
- L. Nachbin, A theorem of Hahn-Banach type for linear transformations, Trans. Amer. Math. Soc. 68 (1950), p. 28-46.
- L. Nachbin, Some problems in extending and lifting continuous linear transformations, Proc. Interm. Symp. on Linear Spaces, Jerusalem 1960, p. 340-351.
- T. Nakayama, On Frobeniusean algebras, I, Ann. of Math. 40 (1939), p. 611-633.
- T. Ohkuma, Duality in mathematical structure. Proc. Japan Acad. 34 (1958), p. 6-10.
- W. Orlicz and V. Pták, Some remarks on Saks spaces, Studia Math, 16 (1957), p. 56-68.
- A. Pełczyński, Projections in certain Banach spares, Studia Math. 19 (1960), p. 209-228.
- R. E. Phelps, Uniqueness of Hahn-Banach extensions and unique best approximation, Trans. Amer. Math. Soc. 95 (1960), p, 238-255.
- J. Rainwater, A note on projective resolutions, Proc. Amor. Math. Soc. 10 (1959), p. 734-735.
- D. Scott, Measurable cardinals and constructive sets, Bull. Acad. Polon. Sci., Sér. des sci. math., astr. et phys. 9 (1961), p. 521-524.
- Z. Semadeni, Embedding of two-norm, spaces into the space of bounded continuous functions on a half-straight line, Bull. Acad. Polon. Sci., Sér. des sci. math., astr. et phys. 8 (1960), p. 421-426.
- Z. Semadeni, Extension of linear functionals in two-norm spaces, Bull. Acad. Polon. Sci., Sér. des sci. math., astr. et phys. 8 (1960), p. 427-432.
- Z. Semadeni, Isomorphic properties of Banaoh spaces of continuous functions, Studia Math, ser. specj., zeszyt 1 (1963), p. 93-108.
- Z. Semadeni, Weak convergence in two-norm spaces and biorthogonal systems, in preparation.
- Z. Semadeni, Free and direct objects, Bull. Amer. Math. Soc. 69 (1963), p. 63-66.
- W. Sierpiński, Sur les projections des ensembles complementaires aux ensembles A, Fund. Math. 11 (1928), p. 117-122.
- R. Sikorski, A theorem on extension of homomorphisms, Ann. Soc. Polon. Math. 21 (1948), p. 322-336.
- R. Sikorski, Boolean Algebras, Ergebn. Math., 1960.
- J. Sonner, On the formal definition of categories, Math. Zeitschrift 80 (1962), p. 163-176.
- M. H. Stone, Algebraic characterization of special Boolean rings, Fund. Math. 29 (1937), p. 223-303.
- M. H. Stone, Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc. 41 (1937), p. 375-481.
- M. H. Stone, Boundedness properties in function lattices, Canadian J. Math. 1 (1949), p. 176-186.
- A. Tarski, Some problems and results relevant to the foundations of the set theory. Proc. Intern. Congress for Logic, Math. and Phil. of Sci., Stanford 1960.
- A. E. Taylor, The extension of linear functionals, Duke Math. J. 5 (1939), p. 538-547.
- A. Wiweger, A topologisation of Saks spaces, Hull. Acad. Polon. Sci., Sér. des sci. math., astr. et phys. 6 (1957), p. 773-777.
- A. Wiweger, Linear spaces with mixed topology, Studia Math. 20 (1961), p. 47-68.
- A. Wiweger, Some applications of mixed topologies, Bull. Acad. Polon. Sci., Sér. des sci. math., astr. et phys., 9 (1961).
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