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Поредното заседание на Общия семинар на секция “Анализ, геометрия и топология” ще се проведе на 14 септември 2021 г. от 14:00 часа в зала 478 на ИМИ.
Доклад на тема:

The Dimension Dind оf Finite Topological T0-Spaces

ще изнесе Dimitrios Georgiou, University of Patras, Greece.

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Резюме. 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.
References:
[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.

Семинарът ще се проведе при спазване на всички противоепидемиологични мерки.