Frame presentations of compact hedgehogs and their properties

Abstract

This paper considers the compact hedgehog as a frame presented by generators and relations, based on the presentation of the frame of extended real numbers. The main focus will be on the point-free version of continuous and semicontinuous functions that arise from it, and their application in  characterizations of variants of collectionwise normality. The variants to be considered are defined by selections of adequate families of sublocales and  their characterizations depend on lattice-theoretic properties of the selected families. This way insertion and extension results for semicontinuous and  continuous functions with values in the compact hedgehog frame are generalized and unified.