On the number of topologies on a finite set

Date

2019-01-01

Author

Kızmaz, Muhammet Yasir

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

202
views

0
downloads

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

Suggestions

OpenMETU
Core

On endomorphisms of surface mapping class groups Korkmaz, Mustafa (Elsevier BV, 2001-05-01) In this paper, we prove that every endomorphism of the mapping class group of an orientable surface onto a subgroup of finite index is in fact an automorphism.
On the influence of fixed point free nilpotent automorphism groups Ercan, Gülin (2017-12-01) A finite group FH is said to be Frobenius-like if it has a nontrivial nilpotent normal subgroup F with a nontrivial complement H such that for all nonidentity elements . Let FH be a Frobenius-like group with complement H of prime order such that is of prime order. Suppose that FH acts on a finite group G by automorphisms where in such a way that In the present paper we prove that the Fitting series of coincides with the intersections of with the Fitting series of G, and the nilpotent length of G exceeds the...
On the arithmetic operations over finite fields of characteristic three with low complexity AKLEYLEK, SEDAT; Özbudak, Ferruh; Özel, Claire Susanna (2014-03-15) In this paper, the Hermite polynomial representation is adapted as a new way to represent certain finite fields of characteristic three. We give the multiplication method to multiply two elements of F-3n in the Hermite polynomial representation with subquadratic computational complexity by using a divide-and-conquer idea. We show that in some cases there is a set of irreducible binomials in the Hermite polynomial representation to obtain modular reduction with a lower addition complexity than the standard p...
On a Fitting length conjecture without the coprimeness condition Ercan, Gülin (Springer Science and Business Media LLC, 2012-08-01) Let A be a finite nilpotent group acting fixed point freely by automorphisms on the finite solvable group G. It is conjectured that the Fitting length of G is bounded by the number of primes dividing the order of A, counted with multiplicities. The main result of this paper shows that the conjecture is true in the case where A is cyclic of order p (n) q, for prime numbers p and q coprime to 6 and G has abelian Sylow 2-subgroups.
On local finiteness of periodic residually finite groups Kuzucouoglu, M; Shumyatsky, P (2002-10-01) Let G be a periodic residually finite group containing a nilpotent subgroup A such that C-G (A) is finite. We show that if [A, A(g)] is finite for any g is an element of G, then G is locally finite.

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.