On T-locally compact spaces

TL;DR

This paper introduces T-locally compact spaces, explores their properties, and distinguishes them from locally compact spaces, showing that T-locally compactness is a topological property not preserved under products.

Contribution

The paper defines T-locally compact spaces and investigates their fundamental properties, highlighting differences from locally compact spaces and establishing T-locally compactness as a topological property.

Findings

Every Hausdorff, locally compact space is T-locally compact.

T-locally compactness is independent of local compactness.

T-locally compactness is not preserved under product topology.

Abstract

The aim of this paper is to introduce and give preliminary investigation of T-locally compact spaces. Locally compact and T-locally compact are independent of each other. Every Hausdorff, locally compact space is T-locally compact. T-locally compact is a topological property. T-locally compact is not preserved by the product topology.