Bagheri Salec, A. (2017). Generated topology on infinite sets by ultrafilters. Sahand Communications in Mathematical Analysis, 08(1), 43-53. doi: 10.22130/scma.2017.23337

Alireza Bagheri Salec. "Generated topology on infinite sets by ultrafilters". Sahand Communications in Mathematical Analysis, 08, 1, 2017, 43-53. doi: 10.22130/scma.2017.23337

Bagheri Salec, A. (2017). 'Generated topology on infinite sets by ultrafilters', Sahand Communications in Mathematical Analysis, 08(1), pp. 43-53. doi: 10.22130/scma.2017.23337

Bagheri Salec, A. Generated topology on infinite sets by ultrafilters. Sahand Communications in Mathematical Analysis, 2017; 08(1): 43-53. doi: 10.22130/scma.2017.23337

Generated topology on infinite sets by ultrafilters

^{}Department of Mathematics, Faculty of Science, University of Qom, P.O.Box 3716146611, Qom, Iran.

Abstract

Let $X$ be an infinite set, equipped with a topology $\tau$. In this paper we studied the relationship between $\tau$, and ultrafilters on $X$. We can discovered, among other thing, some relations of the Robinson's compactness theorem, continuity and the separation axioms. It is important also, aspects of communication between mathematical concepts.

[1] R. Engelking, General Topology, Berlin, Sigma series in pure mathematics, Vol. 6, 1989.

[2] N. Hindman and I. Leader, The semigroup of ultrafilters near 0, Semigroup Forum, 59 (1999), 33-55.

[3] N. Hindman and D. Strauss, Algebra in the Stone-Cech Compactification, Theory and Application, Springer Series in Computational Mathematics, Walter de Gruyter, Berlin, 1998.

[4] M.A. Tootkaboni and T. Vahed, The semigroup of ultrafilters near an idempotent of a semitopological semigroup, Topology and its Applications, Vol 159, Issue 16, (2012), 3494-3503.

[5] Y. Zelenyuk, Ultrafilters and Topologies on Groups, Walter de Gruyter, Berlin, 2011.