Pointfree functional compactness

Abstract

By introducing a conservative notion of functional compactness to frames and using frame-theoretic techniques, we identify two classes of topological spaces that can be densely embedded in functionally compact ones. Since θ-open elements of frames (corresponding in spaces to complements of Velicko’s [15] θ-closed subspaces) play an important role in functional compactness, we also study the concept of co-rigidity in frames and show that it is enjoyed by all θ-open elements of functionally compact frames.