Paracompact like spaces

Abstract EN

In [1] the concept of countably I-compact spaces was introduced.

A decomposition and several characterizations of this class of spaces were also given.

In this paper-analogous to [1]- we introduce the relatively new notion of countably I-paracompact space as the space that is and every countable cover by regular closed subsets of X has a countable locally finite refinement by regular closed subsets whose interiors cover X.

We prove that a space is countably I-paracompact if and only if it is countably S-paracompact and extremally disconnected.

Several characterizations of countably I-paracompactness are also given.

Moreover, we study maps of countably I-paracompact spaces.