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Mathematics of the USSR-Sbornik, 1973, Volume 19, Issue 1, Pages 105–115
DOI: https://doi.org/10.1070/SM1973v019n01ABEH001738
(Mi sm2998)
 

This article is cited in 6 scientific papers (total in 6 papers)

Products of ultrafilters and irresolvable spaces

V. I. Malykhin
References:
Abstract: A space dense in itself is said to be $k$-resolvable if there exists a system of cardinality $k$ of disjoint dense subsets. The main results of the paper can be formulated as follows:
1. If there exists a countably-centered free ultrafilter, then there are dense in themselves $T_1$-spaces whose product is irresolvable.
2. Any sets $X$ and $Y$ support irresolvable $T_1$-topologies whose product is maximally resolvable.
3. Assuming the continuum hypothesis, an ultrafilter whose cartesian square is dominated by only three ultrafilters is constructed on a countable set.
4. If a set of uncountable cardinality supports an ultrafilter whose square is dominated by exactly three ultrafilters, then its cardinality is measurable.
A number of problems are posed.
Bibliography: 9 titles.
Received: 29.05.1972
Bibliographic databases:
UDC: 513.83
MSC: Primary 54B10, 54B15; Secondary 04A30
Language: English
Original paper language: Russian
Citation: V. I. Malykhin, “Products of ultrafilters and irresolvable spaces”, Math. USSR-Sb., 19:1 (1973), 105–115
Citation in format AMSBIB
\Bibitem{Mal73}
\by V.~I.~Malykhin
\paper Products of ultrafilters and irresolvable spaces
\jour Math. USSR-Sb.
\yr 1973
\vol 19
\issue 1
\pages 105--115
\mathnet{http://mi.mathnet.ru//eng/sm2998}
\crossref{https://doi.org/10.1070/SM1973v019n01ABEH001738}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=383330}
\zmath{https://zbmath.org/?q=an:0252.54003}
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  • https://doi.org/10.1070/SM1973v019n01ABEH001738
  • https://www.mathnet.ru/eng/sm/v132/i1/p106
  • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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