α-countably paracompact

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

Definition

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

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

Reference

  • 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