Investigation of One-Point Compactification in Semi-Normal Spaces
Nguli E. *
Department of Pure and Applied Mathematics, Jaramogi Oginga Odinga University of Science and Technology, Box 210-40601, Bondo. Kenya.
Mogotu P.
Department of Pure and Applied Mathematics, Jaramogi Oginga Odinga University of Science and Technology, Box 210-40601, Bondo. Kenya.
Kangogo W.
Department of Pure and Applied Mathematics, Jaramogi Oginga Odinga University of Science and Technology, Box 210-40601, Bondo. Kenya.
*Author to whom correspondence should be addressed.
Abstract
Let X be a non-empty set and (X, τ) be a semi-normal space. In this paper, we investigated the relationship between one-point compactification and semi-normal spaces under the fram.work of semi-open sets. In addition, we in particular proved that if (X, τ) is a semi-normal space, then its one-point compactification, X∗ is also semi-normal. We also extended our work on establishing that, if (X, τ) is a semi-normal space, then its one-point compactification, X∗ of X is compact if and only if (X, τ) is also Hausdorff.
Keywords: Topological space, semi-open set, cover of a set, compact set, one-point compactification, semi-normal space