On CB-compact, countably CB-compact and CB-Lindelöf spaces

Abstract

By a (countably) CB-compact space we call a topological space each cover (respectively each countable cover) of which by open sets with compact boundaries contains a finite subcover. By a CB-Lindelöf space we call a topological space each cover of which by open sets with compact boundaries contains a countable subcover. Basic properties of these spaces and relations of these spaces to some other classes of topological spaces are studied.