Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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ON THE THEORY OF SELECTIONS

  • LEE, SEUNG WOO (Dept. of Mathematics, W onkwang University)
  • Received : 1997.04.11
  • Published : 19970000
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Abstract

In this paper, we give a characterization of collectionwise normality using continuous functions. More precisely, we give a new and short proof of the Dowker's theorem using selection theory that a $T_1$ space X is collectionwise normal if every continuous mapping of every closed subset F of X into a Banach space can be continuously extended over X. This is also a generalization of Tietze's extension theorem.

Keywords

Acknowledgement

Supported by : Wonkwang Universíty Research Grant

References

  1. Amer. J. Math. v.69 Mapping theorems for non-compact spaces C.H. Dowker
  2. General Topology R. Engelking
  3. Ann. of Math. v.63 Continuous selections Ⅰ E. Michael
  4. Ann. of Math. v.64 Continuous selections Ⅱ E. Michael
  5. Duke Math. J. v.26 no.4 A theorem on semi-continuous set-valued functions E. Michael
  6. Infinite Dimensional Topology J. van Mill