Spaces whose Pseudocompact Subspaces are Closed Subsets

Applied General Topology

Jack R. Porter¹  R. Grant Woods²  Alan Dow³  R.M. Stephenson⁴ 

[1] University of Kansas;University of Manitoba;University of North Carolina;University of South Carolina;

关键词: Compact;    Pseudocompact;    Fréchet;    Sequential;    Product;    Extension;   

DOI  :  10.4995/agt.2004.1973

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown