Completion from an abstract perspective (Q1704504)

An overview of compactification methods interesting from both mathematical and methodological points of view. The method is studied in a general setting of an abstract space, consisting of a universe of points and its subsets called domains, where open sets are unions of families of domains. On these spaces continuous functions, homeomorphisms and different types of product spaces (classical, Cartesian, Tichonov) are defined. In order to use generalized sequences, various index schemes (sequential, Cartesian, Moore, transordinal) are defined. The main part of the paper is devoted to formalization of various completion schemes, accompanied with respective examples.