Some refinements of a selection theorem with O-dimensional domain

B. Michael

Fundamenta Mathematicae (1992)

  • Volume: 140, Issue: 3, page 279-287
  • ISSN: 0016-2736

Abstract

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The following known selection theorem is sharpened, primarily, by weakening the hypothesis that all the sets φ(x) are closed in Y: Let X be paracompact with dimX = 0, let Y be completely metrizable and let φ:X → 𝓕(Y) be l.s.c. Then φ has a selection.

How to cite

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Michael, B.. "Some refinements of a selection theorem with O-dimensional domain." Fundamenta Mathematicae 140.3 (1992): 279-287. <http://eudml.org/doc/211946>.

@article{Michael1992,
abstract = {The following known selection theorem is sharpened, primarily, by weakening the hypothesis that all the sets φ(x) are closed in Y: Let X be paracompact with dimX = 0, let Y be completely metrizable and let φ:X → 𝓕(Y) be l.s.c. Then φ has a selection.},
author = {Michael, B.},
journal = {Fundamenta Mathematicae},
keywords = {continuous selections},
language = {eng},
number = {3},
pages = {279-287},
title = {Some refinements of a selection theorem with O-dimensional domain},
url = {http://eudml.org/doc/211946},
volume = {140},
year = {1992},
}

TY - JOUR
AU - Michael, B.
TI - Some refinements of a selection theorem with O-dimensional domain
JO - Fundamenta Mathematicae
PY - 1992
VL - 140
IS - 3
SP - 279
EP - 287
AB - The following known selection theorem is sharpened, primarily, by weakening the hypothesis that all the sets φ(x) are closed in Y: Let X be paracompact with dimX = 0, let Y be completely metrizable and let φ:X → 𝓕(Y) be l.s.c. Then φ has a selection.
LA - eng
KW - continuous selections
UR - http://eudml.org/doc/211946
ER -

References

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  1. [B] D. Burke, Covering properties, in: Handbook of Set-Theoretic Topology, North-Holland, Amsterdam 1984, 347-422. 
  2. [M1] E. Michael, A note on paracompact spaces, Proc. Amer. Math. Soc. 4 (1953), 831-838. Zbl0052.18701
  3. [M2] E. Michael, Selected selection theorems, Amer. Math. Monthly 63 (1956), 233-238. Zbl0070.39502
  4. [M3] E. Michael, Continuous selections I, Ann. of Math. 63 (1956), 361-382. Zbl0071.15902
  5. [M4] E. Michael, Continuous selections II, Ann. of Math. 64 (1956), 562-580. Zbl0073.17702
  6. [M5] E. Michael, The product of a normal space and a metric space need not be normal, Bull. Amer. Math. Soc. 69 (1963), 375-376. Zbl0114.38904
  7. [M6] E. Michael, Continuous selections and countable sets, Fund. Math. 111 (1981), 1-10. Zbl0455.54012
  8. [M7] E. Michael, A generalization of a theorem on continuous selections, Proc. Amer. Math. Soc. 105 (1989), 236-243. Zbl0675.54018

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