Locally Compact Spaces with Defects

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