Uniform Local Connectedness and Completion of Metric σ-Frames

Abstract

ABSTRACT We extend the notion of local connectedness and uniform local connectedness to the category MσFrm of metric σ-frames. We provide the construction of the uniformly locally connected reflection of a locally connected metric σ-frame. We also discuss complete metric σ-frames and show the existence of a completion for a metric σ-frame in the category MσFrm.