Local Connectedness and the Wallman Cmpactification

Abstract

For a regular frame L with a locally connected Wallman basis we obtain several criteria for its corresponding Wallman compacti cation to be perfect and locally connected. We then give an application of this result by proving that the Freudenthal compacti cation of a connected rim-compact frame is locally connected if and only if the frame is locally connected.

Quaestiones Mathematicae 35(2012), 245-257.