σ-metacompact

Definition

A topological space X is σ-metacompact if every open cover of X has an open refinement which is the union of countably many point-finite families.

Remark

• It is also called metaLindelöf? ([Yakovlev]).

Reference

• Reznichenko, E. A.(RS-MOSCM-GT) and Uspenskij, V. V.(RS-MOSCM-GT), Pseudocompact Malʹtsev spaces. (English summary) ,Special issue on topological groups. ,Topology Appl. 86 (1998), no. 1, 83-104.
• N. N. Yakovlev, On bicompacta in Σ-products and related spaces, Comment. Math. Univ. Carolinae, Vol. 21 (1980), No. 2, pp.263-283.