CONTINUOUS SELECTIONS UNDER WEAKER SEPARATION AXIOMS AND REFLEXIVE BANACH SPACES

  • Published : 1999.11.01

Abstract

The paper is devoted to generalizations of continuity of set-valued mappings and some properties of hypertopologies on the collection of some subsets of a topological space. It is also dedicated to continuous selection theorems without relatively higher separation axioms. More precisely, we give characterizations of $\lambda$-collectionwise normality using continuous functions as in Michael's papers.

Keywords

References

  1. Normal topological spaces R. Alo;L. Shapiro
  2. Canad. J. Math. v.5 Extension of coverings, of pseudometris, adn linear-space-valued mappings R. Arens
  3. On the Fell Topology, Set-valued Analysis v.1 G. Beer
  4. Topologices on closed and closed convex sets G. Beer
  5. Trans. Amer. Math. Soc. v.335 Weak topologies on the closed subsets of a metrizable space G. Beer;R. Lucchetti
  6. Ann. Mat. Pura Appl. v.162 no.4 Distance functionals and suprema of hyperspace topologies G. Beer;A. Lechicki;S. Levi;S. Naimpally
  7. General Topology R. Engelking
  8. Proc. Amer. Math. Soc. v.13 A Hausdorff topology for the closed subsets of locally compact non-Hausdorff space J. Fell
  9. Topology and its Appl. v.70 Selections and hyperspace topologies via special metrics V. G. Gutev
  10. Selections without higher separation axioms V. G. Gutev
  11. Selection without higher separation axioms and finite dimensional sets V. G. Gutev
  12. Generic extensions of finite-valued u.s.c. selections V. G. Gutev
  13. Continuous selections and reflexive Banach spaces V. G. Gutev;S. Nedev
  14. J. Convex Anal. v.1 A new approach to a Hyperspace theory R. Lucchetti;A. Pasquale
  15. Trans. Amer. Math. Soc. v.71 Topologies on spaces of subsets E. Micheal
  16. Ann. of Math. v.63 Continuous selections Ⅰ E. Michael
  17. Ann. of Math. v.64 Continuous selections Ⅱ E. Michael
  18. Open Problems in Topology E. Michael;J. van Mill(ed.);J. M. Reed(ed.)
  19. Serdica v.6 Selections and factorization theorems for set-valued mappings S. Nedev
  20. Continuous selections of multivalued mappings D. Repovs;P. V. Semenov
  21. Trans. Amer. Math. Soc. v.340 Set convergences, An attempt of classification Y. Sountag;C. Zalinescu
  22. Trans. Amer. Math. Soc. v.123 convergence of sequences of convex sets, cones, and functions, Ⅱ R. Wijsman