Abstract

In this paper we denote by ((Z2)⁎,(κ2)⁎) the Alexandroff one point compactification of the Khalimsky (K-, brevity) plane. We often call this space the infinite K-topological sphere or the infinite K-sphere for brevity in the present paper. After studying various properties of the infinite K-topological sphere such as a non-Alexandroff structure, we study low and semi-separation axioms of it. Finally, let (X,T) be a topological space which is semi-T2 and each point x(∈X) has an open neighborhood V(∋x) such that the closure of V (or ClX(V)) is compact, and (X⁎,T⁎) an Alexandroff one point compactification of (X,T). Then, we prove that (X⁎,T⁎) is a semi-T2-space. Thus it turns out that the infinite K-sphere is a semi-T2-space.

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