[图书][B] The structure of compact groups: a primer for students-a handbook for the expert
KH Hofmann, SA Morris - 2006 - degruyter.com
In this appendix we shall record background material on abelian groups. We begin by fixing
standard notation and by listing elementary examples. Basically we stay in the domain of …
standard notation and by listing elementary examples. Basically we stay in the domain of …
Minimality conditions in topological groups
D Dikranjan, M Megrelishvili - Recent progress in general topology III, 2013 - Springer
This is a survey on the recent progress in minimal topological groups, with a particular
emphasis on constructions leading to non-abelian minimal groups, as semidirect products …
emphasis on constructions leading to non-abelian minimal groups, as semidirect products …
Independent group topologies on Abelian groups
M Tkachenko, I Yaschenko - Topology and its Applications, 2002 - Elsevier
Two non-discrete T1 topologies τ1, τ2 on a set X are called independent if their intersection
τ1∩ τ2 is the cofinite topology on X. We show that a countable group does not admit a pair …
τ1∩ τ2 is the cofinite topology on X. We show that a countable group does not admit a pair …
Suitable sets for topological groups
WW Comfort, SA Morris, D Robbie, S Svetlichny… - Topology and its …, 1998 - Elsevier
A subset S of a topological group G is said to be a suitable set if (a) it has the discrete
topology,(b) it is a closed subset of G {1}, and (c) the subgroup generated by S is dense in …
topology,(b) it is a closed subset of G {1}, and (c) the subgroup generated by S is dense in …
Long chains of topological group topologies—a continuation
WW Comfort, D Remus - Topology and its Applications, 1997 - Elsevier
We continue the work initiated in our earlier article (J. Pure Appl. Algebra 70 (1991) 53–72);
as there, for G a group let B (G)(respectively N (G)) be the set of Hausdorff group topologies …
as there, for G a group let B (G)(respectively N (G)) be the set of Hausdorff group topologies …
Generating sets for compact semisimple Lie groups
M Field - Proceedings of the American Mathematical Society, 1999 - ams.org
GENERATING SETS FOR COMPACT SEMISIMPLE LIE GROUPS 1. Introduction Suppose that Γ
is a compact connected Lie group of dimension Page 1 PROCEEDINGS OF THE AMERICAN …
is a compact connected Lie group of dimension Page 1 PROCEEDINGS OF THE AMERICAN …
On Model-Theoretic Connected Groups
J Gismatullin - The Journal of Symbolic Logic, 2024 - cambridge.org
We introduce and study the model-theoretic notions of absolute connectedness and type-
absolute connectedness for groups. We prove that groups of rational points of split …
absolute connectedness for groups. We prove that groups of rational points of split …
Countably compact groups satisfying the open mapping theorem
D Dikranjan - Topology and its Applications, 1999 - Elsevier
We discuss the structure and Cartesian products of the countably compact groups G that
satisfy the following forms of the open mapping theorem:(a) every continuous surjective …
satisfy the following forms of the open mapping theorem:(a) every continuous surjective …
Some topological groups with and some without suitable sets
D Dikranjan, M Tkačenko, V Tkachuk - Topology and its Applications, 1999 - Elsevier
If a discrete subset S of a topological group G with identity 1 generates a dense subgroup of
G and S∪{1} is closed in G, then S is called a suitable set for G. We construct in ZFC a …
G and S∪{1} is closed in G, then S is called a suitable set for G. We construct in ZFC a …
Topological groups with thin generating sets
D Dikranjan, M Tkačenko, V Tkachuk - Journal of Pure and Applied Algebra, 2000 - Elsevier
A discrete subset S of a topological group G with identity 1 is called suitable for G if S
generates a dense subgroup of G and S∪{1} is closed in G. We study various algebraic and …
generates a dense subgroup of G and S∪{1} is closed in G. We study various algebraic and …