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Izv. IMI UdGU, 2015, Issue 2(46), Pages 140–148 (Mi iimi314)  

This article is cited in 2 scientific papers (total in 2 papers)

Some properties of open ultrafilters

E. G. Pytkeevab, A. G. Chentsovab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi, 16, Yekaterinburg, 620990, Russia
b Ural Federal University, ul. Mira, 19, Yekaterinburg, 620002, Russia

Abstract: We study the space of ultrafilters for an arbitrary topological space under natural equipment similar to that used in construction of Stone compactum. It is showed that above ultrafilters space is extremely disconnected compactum. We consider the families of sets in the space of ultrafilters majorizing (any time) the filter of open neighborhoods of a fixed point of initial space. Conditions guaranteeing mutually disjointness and distinguishability of sets for the given family are investigated; in particular, a special axiom of separability connected with support of mentioned distinguishability is introduced.

Keywords: neighborhood, topology, ultrafilter, centered system.

Funding Agency Grant Number
Russian Foundation for Basic Research 13-01-00304
13-04-00847


Full text: PDF file (230 kB)
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Document Type: Article
UDC: 517.917
MSC: 54A20
Received: 06.10.2015

Citation: E. G. Pytkeev, A. G. Chentsov, “Some properties of open ultrafilters”, Izv. IMI UdGU, 2015, no. 2(46), 140–148

Citation in format AMSBIB
\Bibitem{PytChe15}
\by E.~G.~Pytkeev, A.~G.~Chentsov
\paper Some properties of open ultrafilters
\jour Izv. IMI UdGU
\yr 2015
\issue 2(46)
\pages 140--148
\mathnet{http://mi.mathnet.ru/iimi314}
\elib{http://elibrary.ru/item.asp?id=25030038}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. E. G. Pytkeev, A. G. Chentsov, “Open ultrafilters and separability with the use of the operation of closure”, Proc. Steklov Inst. Math. (Suppl.), 299, suppl. 1 (2017), 177–190  mathnet  crossref  crossref  mathscinet  isi  elib
    2. E. G. Pytkeev, A. G. Chentsov, “Nekotorye predstavleniya svobodnykh ultrafiltrov”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 26:3 (2016), 345–365  mathnet  crossref  mathscinet  elib
  • Известия Института математики и информатики Удмуртского государственного университета
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