SEPARATION PROPERTIES IN CONSTRUCTIVE TOPOLOGY

Abstract

AbstractThis chapter studies separation properties in topology as done on the basis of the formal system CZF. Until the 1970s, there was only a limited focus on the general notion of a topological space in constructive mathematics, with most attention being paid to metric space notions both in intuitionistic analysis and in Bishop-style constructive analysis. But in later years, because of the development of topos theory, the study of sheaf models, and work on point-free topology, including work on formal topology, the notions of general topology in constructive mathematics have received more attention. This chapter presents a fairly systematic survey of the main separation properties that topological spaces can have in constructive mathematics. These are perhaps the first kinds of properties to consider when moving from the study of metric spaces to the study of general topological spaces.