Document Type : Research Paper


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


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.


Main Subjects

[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.