On a question of E.A. Michael

Vladimir V. Filippov

Commentationes Mathematicae Universitatis Carolinae (2004)

  • Volume: 45, Issue: 4, page 735-737
  • ISSN: 0010-2628

Abstract

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A negative answer to a question of E.A. Michael is given: A convex G δ -subset Y of a Hilbert space is constructed together with a l.s.c. map Y → Y having closed convex values and no continuous selection.

How to cite

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Filippov, Vladimir V.. "On a question of E.A. Michael." Commentationes Mathematicae Universitatis Carolinae 45.4 (2004): 735-737. <http://eudml.org/doc/249356>.

@article{Filippov2004,
abstract = {A negative answer to a question of E.A. Michael is given: A convex $G_\delta $-subset $Y$ of a Hilbert space is constructed together with a l.s.c. map $Y\rightarrow Y$ having closed convex values and no continuous selection.},
author = {Filippov, Vladimir V.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {l.s.c. map; selection; space of probability measures; l.s.c. map; selection; space of probability measures},
language = {eng},
number = {4},
pages = {735-737},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On a question of E.A. Michael},
url = {http://eudml.org/doc/249356},
volume = {45},
year = {2004},
}

TY - JOUR
AU - Filippov, Vladimir V.
TI - On a question of E.A. Michael
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2004
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 45
IS - 4
SP - 735
EP - 737
AB - A negative answer to a question of E.A. Michael is given: A convex $G_\delta $-subset $Y$ of a Hilbert space is constructed together with a l.s.c. map $Y\rightarrow Y$ having closed convex values and no continuous selection.
LA - eng
KW - l.s.c. map; selection; space of probability measures; l.s.c. map; selection; space of probability measures
UR - http://eudml.org/doc/249356
ER -

References

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  1. Michael E.A., Continuous selections, I, Ann. of Math. (1956), 63 361-382. (1956) Zbl0071.15902MR0077107
  2. Michael E.A., Some problems, in: Open Problems in Topology, J. van Mill, G.M. Reed, eds., North Holland, Amsterdam, 1990, pp.271-278. Zbl1074.11018MR1078653
  3. Gutev V.G., Continuous selections, G δ -subsets of Banach spaces and usco mappings, Comment. Math. Univ. Carolinae (1994), 35.3 533-538. (1994) MR1307280
  4. Gutev V.G., Valov V., Continuous selections and C -spaces, Proc. Amer. Math. Soc. (2002), 130 233-242. (2002) Zbl0977.54017MR1855641
  5. Repovš D., Semenov P.V., Continuous selections of multivalued mappings, in: Recent Progress in General Topology, M. Hušek, J. van Mill, eds., Elsevier Science B.V., 2002, pp.424-461. MR1970007
  6. von Weizsäcker H., A note on infinite dimensional convex sets, Math. Scand. (1976), 38 321-324. (1976) MR0428009
  7. Hilton P.J., Wylie S., Homology Theory, Cambridge University Press, New York, 1960. Zbl0163.17803MR0115161

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