Function-space compactifications of function spaces
The paper presents a nice discussion of applications of the theory of continuous lattices in topology and analysis. We mention two pure topological results which are consequences of more general results: (1) If \(X\) and \(Y\) are compact Hausdorff spaces, then the space \(C_k(X,Y)\) of continuous mappings from \(X\) into \(Y\) with the compact-open topology can be embedded into the Vietoris hyperspace over \(X\times Y\) (by the graph mapping); (2) If \(X\) is a locally compact Hausdorff space, then the space \(C_k(X)\) of continuous real-valued functions on \(X\) with the compact open topology has a (Hausdorff) compactification by a space of pairs of semicontinuous extended real-valued mappings.
scientific article; zbMATH DE number 1787509
scientific article