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Trudy Inst. Mat. i Mekh. UrO RAN, 2016, Volume 22, Number 3, Pages 212–225 (Mi timm1337)  

Open ultrafilters and separability with the use of the operation of closure

E. G. Pytkeevab, A. G. Chentsovba

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
b Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg

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 discernibility of (enlarged) “points” of this type. We use nontraditional separability axioms and study their connection with the known axioms $T_0$, $T_1$, and $T_2.$

Keywords: closure, neighborhood, ultrafilter.

Funding Agency Grant Number
Russian Academy of Sciences - Federal Agency for Scientific Organizations
Russian Foundation for Basic Research 16-07-00266
16-01-00505
16-01-00649


DOI: https://doi.org/10.21538/0134-4889-2016-22-3-212-225

Full text: PDF file (217 kB)
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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2017, 299, suppl. 1, 177–190

Bibliographic databases:

Document Type: Article
UDC: 517.917
MSC: 54A10, 54A20
Received: 14.01.2016

Citation: E. G. Pytkeev, A. G. Chentsov, “Open ultrafilters and separability with the use of the operation of closure”, Trudy Inst. Mat. i Mekh. UrO RAN, 22, no. 3, 2016, 212–225; Proc. Steklov Inst. Math. (Suppl.), 299, suppl. 1 (2017), 177–190

Citation in format AMSBIB
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\paper Open ultrafilters and separability with the use of the operation of closure
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\pages 212--225
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