The Stone-Cech Compactification Of Fibrewise Topological Spaces

Abstract

The purpose of this paper is to introduce and investigate new concepts related to fibrewise topological spaces over a base space C. We begin by defining what constitutes a fibrewise topological space and examining its key properties. We then address the notions of compactness and compactification within this context. In particular, we demonstrate that every fibrewise continuous function from A into any fibrewise compact space can be uniquely extended to the largest compactification of A. Several additional results concerning fibrewise compactification are also presented and discussed.