The dimension Dind of finite topological T0-spaces

Abstract

A. V. Arhangelskii introduced the dimension Dind and properties of this dimension have been studied for various classes of topological spaces. In this paper, we study this dimension for finite T0-spaces. Especially, we prove that in the realm of finite T0-spaces, Dind is less than or equal to the small inductive dimension ind, the large inductive dimension Ind and the covering dimension dim. We also study the "gaps"between Dind and the dimensions ind, Ind and dim, presenting various examples which shows these "gaps". Moreover, in this field of spaces, we give characterizations of Dind, inserting the meaning of the maximal family of pairwise disjoint open sets, and study properties of this dimension. © 2022 Mathematical Institute Slovak Academy of Sciences.