On localization of the Menger property

Abstract

In this paper we introduce and study the local version of the Menger property, namely locally Menger property (or, locally Menger space).  We explore some preservation like properties in this space. We also discuss certain situations where this local property behaves  somewhat differently from the classical Menger property. Some observations about the character of a point, network weight and weight  in this space are also investigated carefully. We also introduce the notion of Menger generated space (in short, MG-space) and make  certain investigations in these spaces. Several topological observations on the decomposition and the remainder of locally Menger  spaces are also discussed.