On the number of topologies on a finite set

• Published in: Algebra and Discrete Mathematics
• Date: 2019
• Main Author: Kizmaz, M.Y.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2019
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/188421
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: On the number of topologies on a finite set / M.Y. Kizmaz // Algebra and Discrete Mathematics. — 2019. — Vol. 27, № 1. — С. 50–57. — Бібліогр.: 8 назв. — англ.

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...