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ArticleOriginal scientific text

Title

Some refinements of a selection theorem with O-dimensional domain

Authors 1

Affiliations

  1. Department of Mathematics, University of Washington, Seattle, Washington 98195, U.S.A.

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 → (Y) be l.s.c. Then φ has a selection.

Bibliography

  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.
  3. [M2] E. Michael, Selected selection theorems, Amer. Math. Monthly 63 (1956), 233-238.
  4. [M3] E. Michael, Continuous selections I, Ann. of Math. 63 (1956), 361-382.
  5. [M4] E. Michael, Continuous selections II, Ann. of Math. 64 (1956), 562-580.
  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.
  7. [M6] E. Michael, Continuous selections and countable sets, Fund. Math. 111 (1981), 1-10.
  8. [M7] E. Michael, A generalization of a theorem on continuous selections, Proc. Amer. Math. Soc. 105 (1989), 236-243.

Additional information

http://matwbn.icm.edu.pl/ksiazki/fm/fm140/fm14036.pdf

Fundamenta Mathematicae
1991-1992/140/3
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Pages:
279-287
Main language of publication
English
Received
1991-08-07
Published
1992
Exact and natural sciences