On compactly dominated spaces (Q1821382)

A topological space X is said to be compactly dominated if there is a cover K of X consisting of compact subsets such that each union of K'\(\subset K\) is closed and has the weak topology generated by K' (this concept is useful in dimension theory). (1) X is compactly dominated iff it is a continuous closed image of a locally compact paracompact space (or, of a disjoint sum of compact spaces). (2) The class of compactly dominated spaces is closed hereditary, not hereditary, not finitely productive, not closed under quotients. Examples of standard spaces which are not compactly dominated are given.