On locally LC-spaces

A topological space $(X,\tau )$ is called a locally LC-space if every point of $X$ has a neighborhood $U$ such that every Lindel"{o}f subset of $(U,\tau \mathrm{\mid }U)$ is a closed subset of $(U,\tau \mathrm{\mid }U)$. The aim of this paper is to continue the study of locally LC-spaces.