Locally Compact Spaces with Defects

Authors

  • Mohmmad Zailai King Abdulaziz University

DOI:

https://doi.org/10.29020/nybg.ejpam.v16i2.4767

Keywords:

Locally, compact, defects

Abstract

We call a topological space X a locally compact space with defects if all points in X possess compact neighborhoods except for some points. We investigate this weaker version of local compactness. We show that for x ∈ X• if the partition of singletons of X\(X• ∪ (U\U)) is locally finite, where U ̸= X is an open neighborhood of x, then X is a Tychonoff space. Let X be a T1c locally compact space with defects such that each x ∈ X• has an open neighborhood U such that U is a union of pairwise disjoint compact subsets S s∈S Fs. Then, we show that if the family {Fs}s∈S is locally finite except for a finite number of points, then X is a Tychonoff space.

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Published

2023-04-30

Issue

Section

Nonlinear Analysis

How to Cite

Locally Compact Spaces with Defects . (2023). European Journal of Pure and Applied Mathematics, 16(2), 1228-1235. https://doi.org/10.29020/nybg.ejpam.v16i2.4767