Nigh-Locally Compactness in Topological Spaces

The focus of this paper is the introduction of the notion of a nigh-locally compact topological space. To do this, concepts of "nigh-topological space" and "nigh-compact space" would be defined, and various conclusions and theorems would be derived. This would lead to a well-defined notion of a nigh-locally compact topological space, from which we would obtain a number of theorems and instances concerning this innovative idea.