About Pre-Lindelof Mappings

Abstract

A space can be regarded as a special case of a mapping by identifying the given space with its mapping to a point. This viewpoint leads to the idea of extending to mappings the notions and results established for spaces, which makes it possible to generalize certain results. In this paper, pre-Lindelof mappings are introduced and studied. In particular, it is shown that if the mapping is pre-Lindelof, then pre-Lindelof property converse both to direction of image and to one of preimage.
Key Words: uniform space, uniformly continuous mapping, pre-Lindelof space, pre-Lindelof mapping, uniform cover, topological group, homomorphism.