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- W2951801441 abstract "In this article, we continue our study of Baire one functions on a topological space $X$, denoted by $B_1(X)$ and extend the well known M. H. Stones's theorem from $C(X)$ to $B_1(X)$. Introducing the structure space of $B_1(X)$, it is observed that $X$ may not be embedded inside this structure space. This observation inspired us to build a space $mathcal{M}(B_1(X))/sim$, from the structure space of $B_1(X)$ and to show that $X$ is densely embedded in $mathcal{M}(B_1(X))/sim$. It is further established that it is a $T_0$-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." @default.
- W2951801441 created "2019-06-27" @default.
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- W2951801441 date "2019-06-20" @default.
- W2951801441 modified "2023-09-27" @default.
- W2951801441 title "A T_0 Compactification Of A Tychonoff Space Using The Rings Of Baire One Functions" @default.
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