constructing the banaschewski compactification through the functionally countable subalgebra of c(x)

Let x be a zero-dimensional space and cc(x) denote the functionally countable subalgebra of c(x). it is well known that β0x (the banaschewski compactfication of x) is a quotient space of βx. in this article, we investigate a construction of β0x via βx by using cc(x) which determines the quotient space of βx homeomorphic to β0x. moreover, the construction of v0x via vccx (the subspace {p 2 βx : 8f 2 cc(x), f *(p) < ∞} of βx) is also investigated.