What is Continuity, Constructively?
Peter Schuster (Mathematisches Institut, Universität München, Germany)
Abstract: The concept of continuity for mappings between metric spaces should coincide with that of uniform continuity in the case of a compact domain, and still give rise to a category. In Bishop's constructive mathematics both requests can be fulfilled simultaneously, but then the reciprocal function has to be abandoned as a continuous function unless one adopts the fan theorem. This perhaps little satisfying situation could be avoided by moving to a point-free setting, such as formal topology, in which infinite coverings are defined mainly inductively. The purpose of this paper is to discuss the earlier situation and some recent developments.
Keywords: constructive mathematics, continuity