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Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, 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
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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
Received: 06.10.2015
Bibliographic databases:
Document Type: Article
UDC: 517.917
MSC: 54A20
Language: Russian
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{https://elibrary.ru/item.asp?id=25030038}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Института математики и информатики Удмуртского государственного университета
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