Constructing the Banaschewski compactification through the functionally countable subalgebra of C(X)

Let X be a zero-dimensional space and C_c(X) denote the functionally countable subalgebra of C(X). It is well known that \beta_۰X (the Banaschewski compactfication of X) is a quotient space of \beta X. In this article, we investigate a construction of \beta_۰X via \beta X by using C_c(X) which determines the quotient space of \beta X homeomorphic to  \beta_۰X. Moreover, the construction of  \upsilon_۰X via \upsilon_{_{C_c}}X (the subspace  \{p\in \beta X: \forall f\in C_c(X), f^*(p)<\infty\} of \beta X) is also investigated.

کلیدواژه ها:

Zero-dimensional space ، functionally countable subalgebra ، Stone-rm{check{C}}ech compactification ، Banaschewski compactification