Advertisement

Open Ultrafilters and Separability with the Use of the Operation of Closure

  • E. G. Pytkeev
  • A. G. Chentsov
Article
  • 10 Downloads

Abstract

We study ultrafilters of topologies as well as sets of ultrafilters that each time dominate the open neighborhood filter of some fixed point in a topological space. The sets of ultrafilters are considered as “enlarged points” of the original space. We study conditions that provide the distinguishability of (enlarged) “points” of this type. We use nontraditional separability axioms and study their connection with the known axioms T0, T1, and T2.

Keywords

closure neighborhood ultrafilter. 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    P. S. Aleksandrov, Introduction to the Theory of Sets and General Topology (Editorial URSS, Moscow, 2004) [in Russian].Google Scholar
  2. 2.
    A. G. Chentsov, “Filters and ultrafilters in constructions of attraction sets,” Vestn. Udmurt. Univ., Ser. Mat. Mekh. Komp. Nauki, No. 1, 113–142 (2011).CrossRefMATHGoogle Scholar
  3. 3.
    E. G. Pytkeev and A. G. Chentsov, “Some properties of open ultrafilters,” Izv. Inst. Mat. Inform. Udmurt. Univ., No. 2(46), 140–148 (2015).MATHGoogle Scholar
  4. 4.
    A. V. Bulinskii and A. N. Shiryaev, The Theory of Random Processes (Fizmatlit, Moscow, 2005) [in Russian].Google Scholar
  5. 5.
    R. Engelking, General Topology (Heldermann, Berlin, 1989).MATHGoogle Scholar
  6. 6.
    S. D. Iliadis and S. V. Fomin, “The method of centered systems in the theory of topological spaces,” Russ. Math. Surv. 21 (4), 37–62 (1966).CrossRefMATHGoogle Scholar
  7. 7.
    N. Bourbaki, General Topology (Hermann, Paris, 1940; Nauka, Moscow, 1968).Google Scholar
  8. 8.
    R. A. Aleksandryan and E. A. Mirzakhanyan, General Topology (Vysshaya Shkola, Moscow, 1979) [in Russian].MATHGoogle Scholar
  9. 9.
    A. G. Chentsov and S. I. Morina, Extensions and Relaxations (Kluwer Acad., Dordrecht, 2002).CrossRefMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.Krasovskii Institute of Mathematics and MechanicsUral Branch of the Russian Academy of SciencesYekaterinburgRussia
  2. 2.Ural Federal UniversityYekaterinburgRussia

Personalised recommendations