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countably 3-paracompact

Last-modified: 2015-11-17 (火) 19:16:33

Definition Edit

A subset Y of a space X is said to be countably 3-paracompact in X iff for every countable open cover U of X, there exists a collection V which satisfies:

  1. V consists of open subsets of Y;
  2. V covers Y;
  3. V is a partial refinement? of U;
  4. V is locally finite at Y.

Remark Edit

Reference Edit

K.P.Hart, J. Nagata and J.E. Vaughan, Encyclopedia of general topology, Elsevier Science.