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

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.

UDC: 515.12

Received: 27.10.2021

DOI: 10.55959/MSU0579-9368-1-2023-1-19-25

 English version: Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 2023, 78:1, 21–27

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