2019/06/20 by Ray, A. Deb, Mondal, Atanu
#13A15 #26A21 #54C30 #54C50 #54D35 #FOS: Mathematics #General Topology (math.GN)
paper · doi:10.48550/arxiv.1906.08498
In this article, we continue our study of Baire one functions on a topological space X, denoted by B1(X) and extend the well known M. H. Stones's theorem from C(X) to B1(X). Introducing the structure space of B1(X), it is observed that X may not be embedded inside this structure space. This observation inspired us to build a space M(B1(X))/∼, from the structure space of B1(X) and to show that X is densely embedded in M(B1(X))/∼. It is further established that it is a T0-compactification of X. Such compactification of X possesses the extension property for continuous functions, though it lacks Hausdorffness in general. Therefore, it is natural to search for condition(s) under which it becomes Hausdorff. In the last section, a set of necessary and sufficient conditions for such compactification to become a Stone-Ceck compatification, is finally arrived at.