CONSTRUCTION OF THE SET OF ALL COUNTABLY PARACOMPACT EXTENSIONS

Abstract

One of the central theme in general topology is the theme related to various types of extensions of topological spaces. M. Stone noted that one of the interesting and difficult problems of general topology is the study of all extensions of a given topological spaces. Based on the general problem of M. Stone, B. Banashevsky systematized the general problems of the theory of extensions. P.S. Aleksandfoff posed the problem of classifying compact extensions and formulated various general problems on extensions of topological spaces. A.A. Borubaev, using uniformity, constructed the sets of all paracompact, strongly paracompact, Lindelof and Dieudonne complete extensions of Tychonoff spaces. In this paper, using uniform structures, we construct the sets of all countably paracompact extensions.