Applied General Topology - Vol 05, No 2 (2004)

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  • A fuzzification of the category of M-valued L-topological spaces
  • On separation axioms of uniform bundles and sheaves
  • On the cardinality of indifference classes
  • Resolvability of ball structures
  • Relative Collectionwise Normality
  • Continuous representability of interval orders
  • Which topologies can have immediate successors in the lattice of T1-topologies?
  • Spaces whose Pseudocompact Subspaces are Closed Subsets
  • Two transfinite chains of separation conditions between T1 and T2

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Browsing Applied General Topology - Vol 05, No 2 (2004) by Subject "Compact"

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    Spaces whose Pseudocompact Subspaces are Closed Subsets
    (Universitat Politècnica de València, 2004-10-01) Dow, Alan; Porter, Jack R.; Stephenson, R.M.; Grant Woods, R.; National Science Foundation, EEUU
    [EN] 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.