Some remarks on \(S\)-closed spaces (Q1333070)

A set \(G\) is said to be r-open if and only if it is the interior of a closed set. A filter in \(X\) is said to be r-open if and only if it is generated by a filter base composed of r-open sets. A maximal r-open filter is said to be ultra-r-open. In addition to some characterizations of \(S\)-closed spaces, the purpose of this note is to prove that every space possesses \(S\)-closed extensions. The extension is constructed using ultra-r-open filters.