Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A $T_0$-Compactification Of A Tychonoff Space Using The Rings Of Baire
  One Functions   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.

26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol