Paracompact locally separable spaces, and their images (Q2735460)

Locally separable metric spaces are paracompact locally separable spaces, and some basic properties about locally separable metric spaces hold in paracompact locally separable spaces. In this paper, paracompact locally separable spaces and mapping properties of these spaces are discussed. It contains mapping theorems on paracompact locally separable spaces and metrization theorems on locally separable metric spaces. Some interesting results are obtained about characterizations of images of paracompact locally separable spaces. For example, it is shown that a space is a quotient and \(L\)-image of a paracompact locally separable space if and only if it has a point-countable \(L\)-system; here a map \(f:X\rightarrow Y\) is an \(L\)-map if each \(f^{-1}(y)\) is a Lindelöf subspace of \(X\).