A study of the quasi covering dimension of Alexandroff countable spaces using matrices

Abstract

The notion of Alexandroff space was firstly appeared in [1]. Different types of the covering dimension in the set of all Alexandroff countable spaces have been studied (see [5]). Inspired by [9], where a new topological dimension, called quasi covering dimension was developed, in this paper we study this new dimension in the set of all Alexandroff countable topological spaces using the matrix algebra. Especially, we characterize the open and dense subsets of an arbitrary Alexandroff countable space X using matrices. Under certain additional requirements on X, we provide a computational procedure for the determination of the quasi covering dimension of X.