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The next meeting of the Joint Seminar of Analysis, Geometry and Topology Department will be held on  September 14, 2021 at 14:00 in hall 478 of IMI.

A talk on:

The Dimension Dind оf Finite Topological T0-Spaces

will be delivered by: Dimitrios Georgiou, University of Patras, Greece.

Everybody is invited.

Abstract. A.V. Arhangelskii introduced the dimension Dind [2] and some properties of this dimension have been studied in [1, 3]. In this talk, we present the study of this dimension for finite T0-spaces. Especially, we present 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 give 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 present characterizations of Dind, inserting the meaning of the maximal family of pairwise disjoint open sets, and give properties of this dimension.
[1] Chatyrko V.A., Pasynkov B.A., On sum and product theorems for dimension Dind, Houston J. Math. 28 (2002), no. 1, 119-131.
[2] Egorov V., Podstavkin Ju., A definition of dimension, (Russian) Dokl. Akad. Nauk SSSR 178 1968, 774-777.
[3] Kulpa W., A note on the dimension Dind, Colloq. Math. 24 (1971/72), 181-183.
The results of this talk are the research work of the paper “THE DIMENSION Dind OF FINITE TOPOLOGICAL T0-SPACES”, the authors of which are D. Georgiou, Y. Hattori, A. Megaritis and F. Sereti. This paper has been accepted for publication to the journal Mathematica Slovaca.


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