In previous papers, various notions of (strongly) closed subobject, (strongly) open subobject, connected, compact and Ti, i = 0, 1, 2 objects in a topological category were introduced and compared. The main objective of this paper is to characterize each of these classes of objects in the category of Cauchy spaces as well as to examine how these generalizations are related.
Abstract. In previous papers, various notions of compact, T3, T4, and Tychonoff objects in a topological category were introduced and compared. The main objective of this paper is to characterize each of these classes of objects in the categories of filter and local filter convergence spaces as well as to examine how these various generalizations are related.
An explicit characterization of each of the separation properties Ti, i = 0, 1, Pre T2, and T2 at a point p is given in the topological category of Cauchy spaces. Moreover, specific relationships that arise among the various Ti, i = 0, 1, Pre T2, and T2 structures at p are examined in this category. Finally, we investigate the relationships between generalized separation properties and separation properties at a point p in this category.
In this paper, we characterize local pre-Hausdor¤ extended pseudoquasi-semi metric spaces and investigate the relationships between them. Finally, we show that local pre-Hausdor¤ extended pseudo-quasi-semi metric spaces are hereditary and productive.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.