Discrete reflexivity in function spaces
Discrete reflexivity in function spaces
We study systematically when $C_p(X)$ has a topological property $\mathcal{P}$ if $C_p(X)$ is discretely $\mathcal{P}$, i.e., the set $\overline {D}$ has $\mathcal{P}$ for every discrete subspace $D\subset C_p(X)$. We prove that it is independent of ZFC whether discrete metrizability of $C_p(X)$ implies its metrizability for a compact space $X$. We …