A generalization of local connectedness in Topology

Abstract

Our aim in this paper is to obtain an acceptable generalization of the concept of locally connected spaces in Topology. This is done by utilizing the concept of E-connected spaces which was introduced by Preuss. Locally E-connected spaces are defined and results on locally connected spaces are generalized. In particular, it is shown that the class of all locally E-connected spaces determines a bicoreflective subcategory of Top. From the many examples that are available, we concentrate on those arising from the separation axioms.