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weak cover compact

Last-modified: 2016-04-11 (月) 21:18:57

Definition Edit

A topological space X is weak cover compact if every open cover of X has a weak cover compact open refinement. Here, a "weak cover compact cover" is defined as following. Let V be a cover of X and assume:

  1. V_i is a uncountably infinite collection which consists of distinct members in V;
  2. p_i and q_i are points in V_i without repitition;
  3. a net {p_i} has a limit point.
    If the above conditions impliy the existense of a limit point of {q_i}, we call V weak cover compact.

Remark Edit

  • We will use the abbreviation wcc for weak cover compact.

Reference Edit

  • Mancuso, V. J.,Mesocompactness and related properties, Pacific J. Math. 33 1970 345--355.