Spaces whose Pseudocompact Subspaces are Closed Subsets

• Dow, Alan ^[4] ; Porter, Jack R. ^[1] ; Stephenson, R.M. ^[2] ; Grant Woods, R. ^[3]
  1. [1] University of Kansas

     University of Kansas

     City of Lawrence, Estados Unidos

     
  2. [2] University of South Carolina

     University of South Carolina

     Estados Unidos

     
  3. [3] University of Manitoba

     University of Manitoba

     Canadá

     
  4. [4] University of North Carolina

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• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 5, Nº. 2, 2004, págs. 243-264
• Idioma: inglés
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• Resumen

  • 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.