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2-paracompact

Last-modified: 2010-11-27 (土) 17:39:30

Definition Edit

A subset Y of a space X is said to be 2-paracompact in X iff for every open cover U of X, there exists a collection V which satisfies:

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

Remark Edit

  • This is not a property for topological spaces, but subspaces.
  • The term "2-paracompact" is often shortened to "paracompact".
  • See 1-paracompact, 3-paracompact.

Reference Edit

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