On the number of topologies on a finite set

Date

2019-01-01

Author

Kızmaz, Muhammet Yasir

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We denote the number of distinct topologies which can be defined on a set X with n elements by T(n). Similarly, T-0(n) denotes the number of distinct T-0 topologies on the set X. In the present paper, we prove that for any prime p, T(p(k)) 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 T-0(p + n) T-0(n + 1) (mod p).

Subject Keywords

Topology, Finite sets, T-0 topology, Quality improvement, logistic regression, Decision tree algorithm C5.0, Casting industry

URI

https://hdl.handle.net/11511/54206

Journal

ALGEBRA & DISCRETE MATHEMATICS

Collections

Department of Mathematics, Article

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Citation Formats

M. Y. Kızmaz, “On the number of topologies on a finite set,” ALGEBRA & DISCRETE MATHEMATICS, pp. 50–57, 2019, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/54206.