Continuous selections, G δ -subsets of Banach spaces and usco mappings

Valentin G. Gutev

Commentationes Mathematicae Universitatis Carolinae (1994)

  • Volume: 35, Issue: 3, page 533-538
  • ISSN: 0010-2628

Abstract

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Every l.s.cṁapping from a paracompact space into the non-empty, closed, convex subsets of a (not necessarily convex) G δ -subset of a Banach space admits a single-valued continuous selection provided every such mapping admits a convex-valued usco selection. This leads us to some new partial solutions of a problem raised by E. Michael.

How to cite

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Gutev, Valentin G.. "Continuous selections, $G_\delta $-subsets of Banach spaces and usco mappings." Commentationes Mathematicae Universitatis Carolinae 35.3 (1994): 533-538. <http://eudml.org/doc/247587>.

@article{Gutev1994,
abstract = {Every l.s.cṁapping from a paracompact space into the non-empty, closed, convex subsets of a (not necessarily convex) $G_\delta $-subset of a Banach space admits a single-valued continuous selection provided every such mapping admits a convex-valued usco selection. This leads us to some new partial solutions of a problem raised by E. Michael.},
author = {Gutev, Valentin G.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {set-valued mapping; lower semi-continuous; upper semi-continuous; selection; countable-dimensional space; lower semi-continuous map; upper semi-continuous map; countable-dimensional space; continuous selection},
language = {eng},
number = {3},
pages = {533-538},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Continuous selections, $G_\delta $-subsets of Banach spaces and usco mappings},
url = {http://eudml.org/doc/247587},
volume = {35},
year = {1994},
}

TY - JOUR
AU - Gutev, Valentin G.
TI - Continuous selections, $G_\delta $-subsets of Banach spaces and usco mappings
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1994
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 35
IS - 3
SP - 533
EP - 538
AB - Every l.s.cṁapping from a paracompact space into the non-empty, closed, convex subsets of a (not necessarily convex) $G_\delta $-subset of a Banach space admits a single-valued continuous selection provided every such mapping admits a convex-valued usco selection. This leads us to some new partial solutions of a problem raised by E. Michael.
LA - eng
KW - set-valued mapping; lower semi-continuous; upper semi-continuous; selection; countable-dimensional space; lower semi-continuous map; upper semi-continuous map; countable-dimensional space; continuous selection
UR - http://eudml.org/doc/247587
ER -

References

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  1. Gutev V., Open mappings looking like projections, Set-valued Analysis 1 (1993), 247-260. (1993) Zbl0818.54011MR1249265
  2. Michael E., Continuous selections I, Ann. of Math. 63 (1956), 361-382. (1956) Zbl0071.15902MR0077107
  3. Michael E., Continuous selections II, Ann. of Math. 64 (1956), 562-580. (1956) Zbl0073.17702MR0080909
  4. Michael E., A theorem on semi-continuous set-valued functions, Duke Math. J. 26:4 (1959), 647-656. (1959) Zbl0151.30805MR0109343
  5. Michael E., Continuous selections avoiding a set, Top. Appl. 28 (1988), 195-213. (1988) Zbl0654.54014MR0931523
  6. Michael E., [unknown], in Open problems in Topology, J. van Mill and J.M. Reed, Chapter 17, 272-278, North-Holland, Amsterdam 1990. Zbl1171.90455MR1078636
  7. Michael E., Some refinements of a selection theorem with 0-dimensional domain, Fund. Math. 140 (1992), 279-287. (1992) Zbl0763.54015MR1173768
  8. J. van Mill, Infinite Dimensional Topology, Prerequisites and Introduction, North-Holland, Amsterdam, 1989. Zbl1027.57022MR0977744
  9. Nedev S., Selection and factorization theorems for set-valued mappings, Serdica 6 (1980), 291-317. (1980) Zbl0492.54006MR0644284

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