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Tytuł książki

Pseudo-boundaries and pseudo-interiors for topological convexities

Autorzy

M. Van de Vel

Seria

Rozprawy Matematyczne tom/nr w serii: 210 wydano: 1983

Zawartość

Pełne teksty:
rm21001.pdf

Warianty tytułu

Abstrakty

EN

CONTENTS
0. Introduction......... .............................................................5
1. Topological convexity structures.......................................6
2. Half-spaces and related results......................................12
3. Pseudo-boundaries........................................................25
4. The Krein-Milman theorem.............................................33
5. Pseudo-interiority...........................................................40
6. The existence of pseudo-interior points.........................50
7. Identification of Z-set and Hilbert cubes.........................62
References........................................................................70
Subject index.....................................................................72

Słowa kluczowe

Tematy

Wydawca

Instytut Matematyczny Polskiej Akademii Nauk

Miejsce publikacji

Warszawa

Copyright

Seria

Rozprawy Matematyczne tom/nr w serii: 210

Liczba stron

73

Liczba rozdzia³ów

Opis fizyczny

Dissertationes Mathematicae, Tom CCX

Daty

wydano
1983

Twórcy

autor
M. Van de Vel

Bibliografia

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  • [2] R. H. Bing, Partitioning a set, Bull. Amer. Math. Soc. 55 (1949), p. 1101-1110.
  • [3] T. A. Chapman, Lectures on Hilbert Cube manifolds, regional coference series in mathematics no. 28, Amer. Math. Soc. (1976).
  • [4] E. K. van Douwen, Remote points, Diss. Math. 187 (1981), p. 1-50.
  • [5] B. Fuchssteiner, Verallgemeinter Konvexitätsbegriffe und der Satz von Krein-Milman, Math. Ann. 186 (1970), p. 149-154.
  • [6] J. De Groot, J. M. Aarts, Complete regularity as a separation axiom, Can. J. Math. 21 (1969), p. 96-105.
  • [7] R. E. Jamison, A general theory of convexity, Doct. Diss., Univ. of Washington, Seattle 1974.
  • [8] R. E. Jamison, Some intersection and generation properties of convex sets, Comp. Math. 35 (2) (1977), p. 147-161.
  • [9] D. C. Kay, E. W. Womble, Axiomatic convexity theory and relationships between the Carathéodory, Helly, and Radon numbers, Pacific J. Math. 38 (2) (1971), p. 471-485.
  • [10] J. L. Kelley, I. Namioka, Linear topological spaces. Springer Verlag, New York 1963.
  • [11] V. L. Klee, Convex sets in linear spaces, Duke Math. J. 18 (1951), p. 443-466.
  • [12] V. L. Klee, Separation properties of convex cones, Proc. Amer. Math. Soc. 6 (1955), p. 313-318.
  • [13] V. L. Klee, The structure of semispaces, Math. Scand. 4 (1956), p. 54-64.
  • [14] V. L. Klee, Separation and support properties of convex sets - a survey. Control theory and the calculus of variations (ed. A. V. Balakrishnan), Academic Press (1969), p. 235-303.
  • [15] E. Michael, Topologies on spaces of subsets, Trans. Amer. Math. Soc. 71 (1951), p. 152-182.
  • [16] E. Michael, Continuous selections I, Ann. of Math. 63 (2) (1956), p. 361-382.
  • [17] J. Van Mill, Superextensions of metrizable continua are Hilbert Cubes, Fund. Math. 107 (1980), p. 201 224.
  • [18] J. Van Mill, Supercompactness and Wallman spaces, Mathematical Centre tract 85, Amsterdam 1977.
  • [19] J. Van Mill, M. Van de Vel, Subbases, convex sets, and hyperspaces, Pacific J. Math. 92 (2) (1981), p. 385-402.
  • [20] J. Van Mill, M. Van de Vel, Convexity preserving mappings in subbase convexity theory, Proc. Kon. Ned. Acad. Wet. 81 (1) (1978), p. 76-90.
  • [21] J. Van Mill, M. Van de Vel, On superextensions and hyperspaces, Topological Structures II, Mathematical Centre tract 115, Amsterdam 1979, p. 169-180.
  • [22] J. Van Mill, E. Wattel, An external characterization of spaces which admit binary normal subbases, Amer. J. Math. 100 (1978), p. 987-994.
  • [23] S. B. Nadler, Hyperspaces of sets. Marcel Dekker, New York 1978.
  • [24] S. Nadler, Jr., J. Quinn, N. M. Stavrakis, Hyperspaces of compact convex sets I, Bull. Acad. Polon. Sci., Sér. Sci. Math., Astr. et Phys. 23 (5) (1975), p. 555-559.
  • [25] H. H. Schaefer, Topological vectorspaces. The MacMillan Company, New York 1966.
  • [26] H. Toruńczyk, On CE-images of the Hilbert Cube and characterizations of Q-manifolds, Fund. Math, (to appear).
  • [27] M. Van de Vel, Superextensions and Lefschetz fixed point structures, Fund. Math. 104 (1978), p. 33-48.
  • [28] M. Van de Vel, A Hahn-Banach theorem in subbase convexity theory, Canad J. Math. 32 (4) (1980), p. 804-820.
  • [29] M. Van de Vel, On generalized Whitney mappings (to appear).
  • [30] M. Van de Vel, Finite dimensional convex structures I: general results. Top. Appl. (to appear).
  • [31] M. Van de Vel, A selection theorem for topological convexity structures (to appear).
  • [32] A. Verbeek, Superextensions of topological spaces. Mathematical Centre tract 41, Amsterdam 1972.
  • [33] L. E. Ward, Jr., Topology, Marcel Dekker, New York 1972.
  • [34] L. E. Ward, Jr., A note on Dentrites and Trees, Proc. Amer. Math. Soc. 5 (1954), p. 992-994.
  • [35] E. Wattel, Superextensions embedded in cubes, Mathematical Centre tract 116, Amsterdam 1979, p. 305-317.
  • [36] G. T. Whyburn, Cut points in general topological spaces, Proc. Nat. Acad. Sci. 61 (1968), p. 380-387.

Języki publikacji

EN

Uwagi

ERRATA Page, line: 33₁₃ For: C Read: O Page, line: 69⁸ For: $H_i(X)$ Read: H₁(X) Page, line: 72₄ For: i(C) Read: ∂(C) Page, line: 72₄ For: $i_X(C)$ Read: $∂_X(C)$ Page, line: 72₄ For: i(X,C) Read: ∂(X,C) Page, line: 72₄ For: 5.1 Read: 3.1

Identyfikator YADDA

bwmeta1.element.zamlynska-6d4f7df7-8043-4875-8edd-5233a6c5f0aa

Identyfikatory

ISBN
83-01-03029-1
ISSN
0012-3862

Kolekcja

DML-PL
Zawartość książki

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