monotonically countably compact

Definition

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

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

Remark

• See monotonically compact.

Reference

• H. R. Bennett, K. P. Hart, and D. J. Lutzer, A note on monotonically metacompact spaces, Topology and its Applications, 157(2010), 456-465.
• http://www.math.wm.edu/~lutzer/drafts/BigBushes.pdf (preprint)