Compactifying a convergence space with functions
Let \(f : X \to K\) be a continuous function from a noncompact Hausdorff convergence space \(X\) into a compact Hausdorff topological space \(K\). Let \(Y = \text{cl}_K f[X]\), \(K_X = \{F \subset X : F\) is compact\} and \(S(f) = \bigcap \{\text{cl}_Y f(X - F) : F \in K_X\} \subset K\). \(S(f)\) is a closed compact subset of \(Y\). The author introduces a convergence structure on \(X^f = X \cup S(f)\). The author proves that if \(X\) is LC, then \(X^f\) is a Hausdorff compactification of \(X\). He also shows that \(f\) has a continuous extension to \(X^f\). There are also several related interesting results.
scientific article; zbMATH DE number 930041