Menger remainders of topological groups

Angelo Bella; Seçil Tokgöz; Lyubomyr Zdomskyy

doi:10.1007/s00153-016-0493-8

Menger remainders of topological groups

Angelo Bella
, Seçil Tokgöz
, Lyubomyr Zdomskyy

Division of Topology

University of Catania
University of Vienna

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

In this paper we discuss what kind of constrains combinatorial covering properties of Menger, Scheepers, and Hurewicz impose on remainders of topological groups. For instance, we show that such a remainder is Hurewicz if and only it is σ-compact. Also, the existence of a Scheepers non-σ-compact remainder of a topological group follows from CH and yields a P-point, and hence is independent of ZFC. We also make an attempt to prove a dichotomy for the Menger property of remainders of topological groups in the style of Arhangel’skii.

Original language	English
Pages (from-to)	767-784
Number of pages	18
Journal	Archive for Mathematical Logic
Volume	55
Issue number	5-6
DOIs	https://doi.org/10.1007/s00153-016-0493-8
Publication status	Published - 1 Aug 2016

Keywords

Forcing
Hurewicz space
Menger space
Remainder
Scheepers space
Topological group
Ultrafilter

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10.1007/s00153-016-0493-8

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AU - Tokgöz, Seçil

AU - Zdomskyy, Lyubomyr

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N2 - In this paper we discuss what kind of constrains combinatorial covering properties of Menger, Scheepers, and Hurewicz impose on remainders of topological groups. For instance, we show that such a remainder is Hurewicz if and only it is σ-compact. Also, the existence of a Scheepers non-σ-compact remainder of a topological group follows from CH and yields a P-point, and hence is independent of ZFC. We also make an attempt to prove a dichotomy for the Menger property of remainders of topological groups in the style of Arhangel’skii.

AB - In this paper we discuss what kind of constrains combinatorial covering properties of Menger, Scheepers, and Hurewicz impose on remainders of topological groups. For instance, we show that such a remainder is Hurewicz if and only it is σ-compact. Also, the existence of a Scheepers non-σ-compact remainder of a topological group follows from CH and yields a P-point, and hence is independent of ZFC. We also make an attempt to prove a dichotomy for the Menger property of remainders of topological groups in the style of Arhangel’skii.

KW - Forcing

KW - Hurewicz space

KW - Menger space

KW - Remainder

KW - Scheepers space

KW - Topological group

KW - Ultrafilter

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VL - 55

SP - 767

EP - 784

JO - Archive for Mathematical Logic

JF - Archive for Mathematical Logic

IS - 5-6

ER -

Menger remainders of topological groups

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Keywords

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