Menger remainders of topological groups

被引：7

作者：

Bella, Angelo ^{[1
]}

Tokgoz, Secil ^{[2
]}

Zdomskyy, Lyubomyr ^{[3
]}

机构：

[1] Univ Catania, Dept Math & Comp Sci, Viale A Doria 6, I-95125 Catania, Italy

[2] Hacettepe Univ, Dept Math, Fac Sci, TR-06800 Beytepe, Turkey

[3] Univ Vienna, Kurt Godel Res Ctr Math Log, Wahringer Str 25, A-1090 Vienna, Austria

来源：

ARCHIVE FOR MATHEMATICAL LOGIC | 2016年 / 55卷 / 5-6期

基金：

奥地利科学基金会;

关键词：

Remainder; Topological group; Menger space; Hurewicz space; Scheepers space; Ultrafilter; Forcing; COMBINATORICS;

D O I：

10.1007/s00153-016-0493-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 -compact. Also, the existence of a Scheepers non--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.

引用

页码：767 / 784

页数：18

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