M. Badie

[ 1 ] - Connections between C(X) and C(Y), where Y is a subspace of X

In this paper, we introduce a method by which we can find a close connection between the set of prime $z$-ideals of $C(X)$ and the same of $C(Y)$, for some special subset $Y$ of $X$. For instance, if $Y=Coz(f)$ for some $fin C(X)$, then there exists a one-to-one correspondence between the set of prime $z$-ideals of $C(Y)$ and the set of prime $z$-ideals of $C(X)$ not containing $f$. Moreover, c...