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1-countably paracompact

Last-modified: 2010-08-14 (土) 00:44:55

Definition Edit

A subspace Y of a space X is 1-countably paracompact in X if for every countable open cover U of X, there exists a collection V of open subsets of X with imgtex.fcgi?%5bres=100%5d%7b$X=%5ccup%20%5cmathcal%7bV%7d$%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

  • Y. Yasui, Results on relatively countably paracompact spaces, Questions Answers Gen. Topology, 17 (1999), 165-174.
  • Y. Yasui, Characterizations of relatively countably paracompact spaces, Memoirs of Osaka Kyoiku University, Ser III, 50 (2001), 1-13.
  • S. Kawaguchi, Results on relative expandability and relative pseudocompactness, Kyoto Univ. RIMS Kokyuroku, Vol.1492 (2006) pp.104-119