The smallest subring of the ring \(C_ p(C_ p(X))\) containing X\(\cup \{1\}\) is everywhere dense in \(C_ p(C_ p(X))\)
A Tikhonov space X is called k-separable if it contains a dense countable union of compact sets. It is shown that if X is k-separable then so is \(C_ p(C_ p(X))\) (the converse is not true). This result follows from the following one: If \(Y\subset X\) then the smallest ring in \(C_ p(C_ p(X))\) containing Y and all constant functions is dense in \(C_ p(C_ p(X))\) iff Y is dense in X.
scientific article; zbMATH DE number 4013509