Function spaces which are stratifiable
It is well-known that if \(X\) is a compact metric and \(Y\) a stratifiable space, \(C(X,Y)\) with the compact-open topology may fail to be stratifiable. The following is proved here. Theorem: Let \(X\) be a compact metric space which has a \(\sigma\)-\(CP\)-\(CF\) quasi-base consisting of closed sets. Then \(C(X,Y)\) has a \(\sigma\)-\(CP\) quasi-base; hence, it is stratifiable. Example: If \(X = \{0\} \cup \{{1 \over n} |n = 1,2, \ldots\}\) is the space of a convergent sequence there exists a countable Lashnev space \(Y\) such that \(C(X,Y)\) is not stratifiable.
scientific article; zbMATH DE number 729225