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countably Aull-pracompact

Last-modified: 2010-08-22 (日) 00:36:58

Definition Edit

A subspace Y is defined to be countably Aull-pamcompact in a topological space X if for every countable collection U of open subsets of X with imgtex.fcgi?%5bres=100%5d%7b$Y%5csubset%5ccup%20%5cmathcal%7bU%7d$%7d%25.png, there exists a collection V of open subsets of X with imgtex.fcgi?%5bres=100%5d%7b$Y%5csubset%5ccup%20%5cmathcal%7bV%7d$%7d%25.png such that V is a partial refinement? of U and V is locally finite at each point of Y.

Remark Edit

  • It is not a property for topological spaces but subspaces.

Reference Edit

  • S. Kawaguchi, Results on relative expandability and relative pseudocompactness, Kyoto Univ. RIMS Kokyuroku, Vol.1492 (2006) pp.104-119