Spaces whose Pseudocompact Subspaces are Closed Subsets

Authors

  • Alan Dow University of North Carolina
  • Jack R. Porter University of Kansas
  • R.M. Stephenson University of South Carolina
  • R. Grant Woods University of Manitoba

DOI:

https://doi.org/10.4995/agt.2004.1973

Keywords:

Compact, Pseudocompact, Fréchet, Sequential, Product, Extension

Abstract

Every first countable pseudocompact Tychonoff space X has the property that every pseudocompact subspace of X is a closed subset of X (denoted herein by “FCC”). We study the property FCC and several closely related ones, and focus on the behavior of extension and other spaces which have one or more of these properties. Characterization, embedding and product theorems are obtained, and some examples are given which provide results such as the following. There exists a separable Moore space which has no regular, FCC extension space. There exists a compact Hausdorff Fréchet space which is not FCC. There exists a compact Hausdorff Fréchet space X such that X, but not X2, is FCC.

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Author Biographies

Alan Dow, University of North Carolina

Department of Mathematics

Jack R. Porter, University of Kansas

Department ofMathematics

R.M. Stephenson, University of South Carolina

Department ofMathematics

R. Grant Woods, University of Manitoba

Department of Mathematics

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How to Cite

[1]
A. Dow, J. R. Porter, R. Stephenson, and R. Grant Woods, “Spaces whose Pseudocompact Subspaces are Closed Subsets”, Appl. Gen. Topol., vol. 5, no. 2, pp. 243–264, Oct. 2004.

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