The dimension Dind of finite topological <i>T</i> <sub>0</sub>-spaces-Reference-Cited by-同舟云学术

The dimension Dind of finite topological T ₀-spaces

Published:2022-06-01 Issue:3 Volume:72 Page:813-829
ISSN:0139-9918
Container-title:Mathematica Slovaca
language:en
Short-container-title:

Author:

Georgiou Dimitrios N.¹,Hattori Yasunao²,Megaritis Athanasios C.³,Sereti Fotini¹

Affiliation:

1. Department of Mathematics , University of Patras , 26500 , Patra , Greece

2. Shimane University , Matsue , Shimane 690-8504 , Japan

3. Department of Physics , University of Thessaly , 35100 , Lamia , Greece

Abstract

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 T 0-spaces. Especially, we prove that in the realm of finite T 0-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.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/ms-2022-0056/pdf

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