Pseudocompact spaces $X$ and $df$-spaces $C_{c}\left ( X\right ) $
Pseudocompact spaces $X$ and $df$-spaces $C_{c}\left ( X\right ) $
Let $X$ be a completely regular Hausdorff space, and let $C_{c}\left ( X\right )$ be the space $C\left ( X\right )$ of continuous real-valued functions on $X$ endowed with the compact-open topology. We find various equivalent conditions for $C_{c}\left ( X\right )$ to be a $df$-space, resolving an old question …