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.

引用

页码：767 / 784

页数：18

共 50 条

[1] Menger remainders of topological groups
Angelo Bella
Seçil Tokgöz
Lyubomyr Zdomskyy
Archive for Mathematical Logic, 2016, 55 : 767 - 784
[2] Remainders of topological and paratopological groups
Xie, Li-Hong
Lin, Shou
TOPOLOGY AND ITS APPLICATIONS, 2013, 160 (04) : 648 - 655
[3] A study of remainders of topological groups
Arhangel'skii, A. V.
FUNDAMENTA MATHEMATICAE, 2009, 203 (02) : 165 - 178
[4] Remainders in compactifications of topological groups
Liu, Chuan
TOPOLOGY AND ITS APPLICATIONS, 2009, 156 (05) : 849 - 854
[5] A note on topological groups and their remainders
Peng, Liang-Xue
He, Yu-Feng
CZECHOSLOVAK MATHEMATICAL JOURNAL, 2012, 62 (01) : 197 - 214
[6] A note on topological groups and their remainders
Liang-Xue Peng
Yu-Feng He
Czechoslovak Mathematical Journal, 2012, 62 : 197 - 214
[7] A theorem on remainders of topological groups
Arhangel'skii, A. V.
van Mill, J.
TOPOLOGY AND ITS APPLICATIONS, 2017, 220 : 189 - 192
[8] Remainders of topological groups and of their subspaces
Arhangel'skii, Alexander Vladimirovich
COMPTES RENDUS DE L ACADEMIE BULGARE DES SCIENCES, 2008, 61 (01): : 5 - 8
[9] Two types of remainders of topological groups
Arhangel'skii, A., V
COMMENTATIONES MATHEMATICAE UNIVERSITATIS CAROLINAE, 2008, 49 (01): : 119 - 126
[10] LOCAL PROPERTIES ON THE REMAINDERS OF THE TOPOLOGICAL GROUPS
Lin, Fucai
KODAI MATHEMATICAL JOURNAL, 2011, 34 (03) : 505 - 518

← 1 2 3 4 5 →