Σ -products and selections of set-valued mappings

Ivailo Shishkov

Commentationes Mathematicae Universitatis Carolinae (2001)

  • Volume: 42, Issue: 1, page 203-207
  • ISSN: 0010-2628

Abstract

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Every lower semi-continuous closed-and-convex valued mapping Φ : X → 2 Y , where X is a Σ -product of metrizable spaces and Y is a Hilbert space, has a single-valued continuous selection. This improves an earlier result of the author.

How to cite

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Shishkov, Ivailo. "$\Sigma $-products and selections of set-valued mappings." Commentationes Mathematicae Universitatis Carolinae 42.1 (2001): 203-207. <http://eudml.org/doc/248761>.

@article{Shishkov2001,
abstract = {Every lower semi-continuous closed-and-convex valued mapping $\Phi : X\rightarrow 2^\{Y\}$, where $X$ is a $\Sigma $-product of metrizable spaces and $Y$ is a Hilbert space, has a single-valued continuous selection. This improves an earlier result of the author.},
author = {Shishkov, Ivailo},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {set-valued mapping; l.s.c. mapping; $\Sigma $-product; selection; set-valued map; selection; l.s.c. mapping; -product},
language = {eng},
number = {1},
pages = {203-207},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {$\Sigma $-products and selections of set-valued mappings},
url = {http://eudml.org/doc/248761},
volume = {42},
year = {2001},
}

TY - JOUR
AU - Shishkov, Ivailo
TI - $\Sigma $-products and selections of set-valued mappings
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2001
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 42
IS - 1
SP - 203
EP - 207
AB - Every lower semi-continuous closed-and-convex valued mapping $\Phi : X\rightarrow 2^{Y}$, where $X$ is a $\Sigma $-product of metrizable spaces and $Y$ is a Hilbert space, has a single-valued continuous selection. This improves an earlier result of the author.
LA - eng
KW - set-valued mapping; l.s.c. mapping; $\Sigma $-product; selection; set-valued map; selection; l.s.c. mapping; -product
UR - http://eudml.org/doc/248761
ER -

References

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  1. Bing R.H., Metrization of topological spaces, Canad. J. Math. 3 (1951), 175-186. (1951) Zbl0042.41301MR0043449
  2. Choban M., Nedev S., Continuous selections for mappings with generalized ordered domain, Math. Balkanica, New Series 11 , Fasc. 1-2 (1997), 87-95. (1997) Zbl0943.46003MR1606612
  3. Corson H., Normality of subsets of product spaces, Amer. J. Math. 81 (1959), 785-796. (1959) MR0107222
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  5. Engelking R., General Topology, PWN, Warszawa, 1985. Zbl0684.54001
  6. Gul'ko S.P., Properties of sets lying in Σ -products, Dokl. AN SSSR, 1977. 
  7. Ishii T., Paracompactness of topological completions, Fund. Math. 92 (1976), 65-77. (1976) Zbl0354.54009MR0418039
  8. Katětov M., On the extension of locally finite coverings (in Russian), Colloq. Math. 6 (1958), 145-151. (1958) MR0103450
  9. Michael E., Continuous selections: I, Ann. Math. 63 (1956), 562-590. (1956) Zbl0071.15902MR0077107
  10. Rudin M.E., Σ -products of metric spaces are normal, preprint (see [5], the problems to Chapter 4). 
  11. Shishkov I., Extensions of l.s.c. mappings into reflexive Banach spaces, Set-Valued Analysis, to appear. Zbl1018.54012MR1888457
  12. Shishkov I., Selections of l.s.c. mappings into Hilbert spaces, Compt. rend. Acad. Bulg. Sci. 53.7 (2000). (2000) MR1779519

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