Weak continuity properties of topologized groups

被引：17

作者：

Cao, J. ^{[1
]}

Drozdowski, R. ^{[2
]}

Piotrowski, Z. ^{[3
]}

机构：

[1] Auckland Univ Technol, Sch Comp & Math Sci, Auckland 1142, New Zealand

[2] Pedag Univ Slupsk, Inst Math, PL-76200 Slupsk, Poland

[3] Youngstown State Univ, Dept Math, Youngstown, OH 44555 USA

来源：

CZECHOSLOVAK MATHEMATICAL JOURNAL | 2010年 / 60卷 / 01期

关键词：

developability number; feebly continuous; nearly continuous; Novak number; paratopological group; semitopological group; topological group;

D O I：

10.1007/s10587-010-0004-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We explore (weak) continuity properties of group operations. For this purpose, the Novak number and developability number are applied. It is shown that if (G, center dot, tau) is a regular right (left) semitopological group with dev(G) < Nov(G) such that all left (right) translations are feebly continuous, then (G, center dot, tau) is a topological group. This extends several results in literature.

引用

页码：133 / 148

页数：16

共 50 条

[41] ROTATING CONTINUITY GROUPS
SACHS, K
ARTESANI, O
FIORE, P
ELETTROTECNICA, 1990, 77 (10): : 965 - 975
[42] CONTINUITY AND HOMEOMORPHISM GROUPS
ELLIS, R
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1953, 4 (06) : 969 - 973
[43] The Continuity of Inverse in Groups
E. A. Reznichenko
Moscow University Mathematics Bulletin, 2022, 77 : 199 - 203
[44] The Continuity of Inverse in Groups
Reznichenko, E. A.
MOSCOW UNIVERSITY MATHEMATICS BULLETIN, 2022, 77 (04) : 199 - 203
[45] Upper and Lower Weak ( τ 1 , τ2)-continuity 2 )- continuity
Thongmoon, Montri
Sompong, Supannee
Boonpok, Chawalit
EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS, 2024, 17 (03): : 1705 - 1716
[46] Weak separation properties for closed subgroups of locally compact groups
Tanko, Zsolt
STUDIA MATHEMATICA, 2017, 238 (02) : 177 - 200
[47] WEAK CONTINUITY AND WEAK LOWER SEMICONTINUITY FOR SOME COMPENSATION OPERATORS
PEDREGAL, P
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1989, 113 : 267 - 279
[48] Weak forms of (Λ, b)-open sets and weak (Λ, b)-continuity
Boonpok, Chawalit
Srisarakham, Napassanan
EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS, 2023, 16 (01): : 29 - 43
[49] Weak continuity on generalized topological spaces
Min, W. K.
ACTA MATHEMATICA HUNGARICA, 2009, 124 (1-2) : 73 - 81
[50] Comparisons of some weak forms of continuity
E. Yang
Acta Mathematica Hungarica, 2007, 116 : 265 - 271

← 1 2 3 4 5 →