Menger remainders of topological groups

被引：6
|
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.
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页码：767 / 784
页数：18
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