Some properties of paracompact locally cosmic spaces (Q2719944)

A space is called a cosmic space if it is a regular space with a countable network. In this paper some properties of paracompact locally cosmic spaces are studied. The author obtains a characterization theorem and some mapping theorems on paracompact locally cosmic spaces, and establishes characterizations of images of paracompact locally cosmic spaces under some sequence-covering and L-mappings. For example, a regular space \(X\) is an image of a paracompact locally cosmic space under a sequentially quotient and L-mapping if and only if \(X\) has a point-countable \(cs^*\)-cover consisting of cosmic subspaces.