Notes on point-free real functions and sublocales

Abstract

Using the technique of sublocales we present a survey of some known facts (with a few new ones added) on point-free real functions. The subjects treated are, e.g., images and preimages, semicontinuity, algebraic structure (point-free real arithmetics), zero and cozero parts, z-embeddings, z-open and z-closed maps, disconnectivity, small sublocales and supports.