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monotonically compact

Last-modified: 2010-09-20 (月) 13:01:18

Definition Edit

A topological space X is said to be monotonically compact if there is a function m on the set of open covers of X (which is called a monotone compactness operator) such that:

  1. if U is an open cover of X, then m(U) is a finite open cover of X which refines U;
  2. if U and V are open covers of X with U refining V, then m(U) refines m(V).

Remark Edit

Reference Edit