strong cover compact

Definition

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

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

Remark

• We will use the abbreviation scc for strong cover compact.

Reference

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