Characterizations of Strongly Paracompact Spaces

Abstract EN

Characterizations of strongly compact spaces are given based on the existence of a star-countable open refinement for every increasing open cover.

It is proved that a countably paracompact normal space (a perfectly normal space or a monotonically normal space) is strongly paracompact if and only if every increasing open cover of the space has a star-countable open refinement.

Moreover, it is shown that a space is linearly D provided that every increasing open cover of the space has a point-countable open refinement.