An answer to A.D Wallace's question about countably compact cancellative semigroups

被引：23
作者：
Robbie, D
Svetlichny, S
机构：
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 1996年 / 124卷 / 01期
关键词：
countably compact space; topological group; cancellative topological semigroup; Abelian group;
D O I：
10.1090/S0002-9939-96-03418-1
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
It is shown under CH that there exists a countably compact topological semigroup with two-sided cancellation which is not a topological group. ''Wallace's question'' of 40 years standing is thus settled in the negative unless CH is explicitly denied. The example is a topological subsemigroup of an uncountabie product of circle groups.
引用
收藏
页码：325 / 330
页数：6
相关论文
共 12 条
[1]   ANOTHER NOTE ON THE CONTINUITY OF THE INVERSE [J].
BRAND, N .
ARCHIV DER MATHEMATIK, 1982, 39 (03) :241-245
[2]  
Comfort W. W., 1984, HDB SET THEORETIC TO, P1143
[3]  
COMFORT WW, 1990, OPEN PROBLEMS TOPOLO, P33
[4]   ON THE EMBEDDING OF TOPOLOGICAL SEMIGROUPS AND INTEGRAL DOMAINS [J].
GELBAUM, B ;
KALISCH, GK ;
OLMSTED, JMH .
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1951, 2 (05) :807-821
[5]   SEQUENTIALLY COMPACT CANCELLATIVE TOPOLOGICAL SEMIGROUPS - SOME PROGRESS ON THE WALLACE PROBLEM [J].
GRANT, DL .
PAPERS ON GENERAL TOPOLOGY AND APPLICATIONS, 1993, 704 :150-154
[6]   SOME NONMETRIC, 1ST COUNTABLE, CANCELLATIVE TOPOLOGICAL SEMIGROUPS THAT ARE GENERALIZED METRIC-SPACES [J].
HEATH, RW .
TOPOLOGY AND ITS APPLICATIONS, 1992, 44 (1-3) :167-173
[7]  
Mukherjea A., 1972, J AUSTR MATH SOC, V13, P180, DOI 10.1017/S1446788700011253
[8]   CONTINUITY OF THE INVERSE [J].
PFISTER, H .
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1985, 95 (02) :312-314
[9]  
TKACHENKO MG, 1990, IZVESTIYA V U Z MATE, V34, P68
[10]  
TOMITA AH, 1994, EXTENDING ROBBIE SVE
12