Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2023, Number 1, Pages 19–25
DOI: https://doi.org/10.55959/MSU0579-9368-1-2023-1-19-25 (Mi vmumm4513) 		 
Mathematics

New properties of topological spaces generalizing extreme non-connectivity

A. Yu. Groznova, O. V. Sipacheva

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
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DOI: https://doi.org/10.55959/MSU0579-9368-1-2023-1-19-25
Abstract: New classes $R_1$, $R_2$, $R_3$ of topological spaces generalizing the class of $F$-spaces are introduced. It is proved that all homogeneous compact subspaces of spaces in these classes and of some of their products are finite. Results on the Rudin–Keisler comparability of ultrafilters along which distinct sequences converge to the same point in $R_2$- and $R_3$-spaces are obtained.
Key words: $F$-space, $\beta\omega$-space, $R_1$-space, $R_2$-space, $R_3$-space, homogeneous compact space, ultrafilter, Rudin–Keisler order.
Received: 27.10.2021
English version:
Moscow University Mathematics Bulletin, 2023, Volume 78, Issue 1, Pages 21–27
DOI: https://doi.org/10.3103/S0027132223010047
Bibliographic databases:
Document Type: Article
UDC: 515.12
Language: Russian
Citation: A. Yu. Groznova, O. V. Sipacheva, “New properties of topological spaces generalizing extreme non-connectivity”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2023, no. 1, 19–25; Moscow University Mathematics Bulletin, 78:1 (2023), 21–27
Citation in format AMSBIB
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\by A.~Yu.~Groznova, O.~V.~Sipacheva
\paper New properties of topological spaces generalizing extreme non-connectivity
\jour Vestnik Moskov. Univ. Ser.~1. Mat. Mekh.
\yr 2023
\issue 1
\pages 19--25
\mathnet{http://mi.mathnet.ru/vmumm4513}
\crossref{https://doi.org/10.55959/MSU0579-9368-1-2023-1-19-25}
\zmath{https://zbmath.org/?q=an:7711500}
\elib{https://elibrary.ru/item.asp?id=50317689}
\transl
\jour Moscow University Mathematics Bulletin
\yr 2023
\vol 78
\issue 1
\pages 21--27
\crossref{https://doi.org/10.3103/S0027132223010047}
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