Please use this identifier to cite or link to this item:
http://hdl.handle.net/123456789/4396
Title: | On the number of topologies on a finite set |
Authors: | Kizmaz, M. Y. |
Keywords: | topology finite sets T0 topology |
Issue Date: | 2019 |
Series/Report no.: | Математичні науки; |
Abstract: | We denote the number of distinct topologies which can be defined on a set X with n elements by T(n). Similarly, T0(n) denotes the number of distinct T0 topologies on the set X. In the present paper, we prove that for any prime p, T(pk ) ≡ k +1 (mod p), and that for each natural number n there exists a unique k such that T(p + n) ≡ k (mod p). We calculate k for n = 0, 1, 2, 3, 4. We give an alternative proof for a result of Z. I. Borevich to the effect that T0(p + n) ≡ T0(n + 1) (mod p). |
Description: | Kizmaz M. Y. On the number of topologies on a finite set / M. Y. Kizmaz // Algebra and Discrete Mathematics. - 2019. - Vol. 27. - Number 2. - Рp.50-57 |
URI: | http://hdl.handle.net/123456789/4396 |
Appears in Collections: | Algebra and Discrete Mathematics. - № 1 (27). - 2019 |
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437-3975-1-PB.pdf | 330 kB | Adobe PDF | View/Open |
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