Tychonoff Objects in the Topological Category of Cauchy Spaces

Abstract

There are various forms of Tychonoff objects for an arbitrary set-based topological category. In this paper, any explicit characterization of each of the Tychonoff Objects is given in the topological category of Cauchy spaces. Moreover, we characterize each of them for the category of Cauchy spaces and investigate the relationships among the various T i , i = 0, 1, 2, 3, 4, P reT 2 , and T 2 (we will refer to it as the usual one) structures are examined in this category.