LAUSR

Abstract In this paper we denote by ( ( Z 2 ) ⁎ , ( κ 2 ) ⁎ ) 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- T 2 and each point x ( ∈ X ) has an open neighborhood V ( ∋ x ) such that the closure of V (or C l X ( V ) ) is compact, and ( X ⁎ , T ⁎ ) an Alexandroff one point compactification of ( X , T ) . Then, we prove that ( X ⁎ , T ⁎ ) is a semi- T 2 -space. Thus it turns out that the infinite K-sphere is a semi- T 2 -space.