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α-countably paracompact

Last-modified: 2010-08-13 (金) 02:12:37

Definition Edit

A subspace Y of a space X is α-countably paracompact in 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 such that imgtex.fcgi?%5bres=100%5d%7b$Y%5csubset%5ccup%20%5cmathcal%7bV%7d$%7d%25.png, V is a partial refinement? of U and V is locally finite in X.

Remark Edit

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

Reference Edit

  • C.E. Aull, Paracompact subsets, Proc. the Second Prague Topological Symposium, 45-51, Prague, 1966.
  • S. Kawaguchi, Results on relative expandability and relative pseudocompactness, Kyoto Univ. RIMS Kokyuroku, Vol.1492 (2006) pp.104-119