nearly metacompact

Definition

A regular Hausdorff space X is said to be nearly metacompact provided that for each open cover C of X there is a dense set D and an open refinement R of C so that R is point finite on D.

Reference

• R.W. Heath and W.F. Lindgren, On generating non-orthocompact spaces, Set-theoretic topology, (Papers, Inst. Medicine and Math., Ohio Univ., Athens, Ohio, 1975-1976), 225-237, Academic Press, New York, 1977.
• Hans-Peter Kunzi and Peter Fletcher, Some Questions Related to Almost 2-Fully Normal Spaces, Rocky Mountain J. Math. Vol.15 (Nov. 1985).