scholarly journals The maximal totally bounded group topology on G and the biggest minimal G-space, for Abelian groups G

1990 ◽  
Vol 34 (1) ◽  
pp. 69-91 ◽  
Author(s):  
Eric K. van Douwen
Keyword(s):  
Abelian Groups ◽  
Group Topology ◽  
Totally Bounded ◽  
Bounded Group ◽  
Totally Bounded Group

Intervals of Totally Bounded Group Topologies

1996 ◽  
Vol 806 (1 Papers on Gen) ◽  
pp. 121-129 ◽  
Author(s):  
W.W. COMFORT ◽  
DIETER REMUS
Keyword(s):  
Totally Bounded ◽  
Bounded Group ◽  
Totally Bounded Group

scholarly journals Totally bounded group topologies and closed subgroups

1982 ◽  
Vol 101 (1) ◽  
pp. 123-132 ◽  
Author(s):  
S. Janakiraman ◽  
T. Soundararajan
Keyword(s):  
Totally Bounded ◽  
Bounded Group ◽  
Totally Bounded Group

scholarly journals TΩ-sequences in abelian groups

2000 ◽  
Vol 24 (3) ◽  
pp. 145-148 ◽  
Author(s):  
Robert Ledet ◽  
Bradd Clark
Keyword(s):  
Abelian Group ◽  
Fundamental System ◽  
Abelian Groups ◽  
Group Topology ◽  
Hausdorff Group

A sequence in an abelian group is called aT-sequence if there exists a Hausdorff group topology in which the sequence converges to zero. This paper describes the fundamental system for the finest group topology in which this sequence converges to zero. A sequence is aTΩ-sequence if there exist uncountably many different Hausdorff group topologies in which the sequence converges to zero. The paper develops a condition which insures that a sequence is aTΩ-sequence and examples ofTΩ-sequences are given.

scholarly journals Algebraic obstructions to sequential convergence in Hausdorrf abelian groups

1998 ◽  
Vol 21 (1) ◽  
pp. 93-96 ◽  
Author(s):  
Bradd Clark ◽  
Sharon Cates
Keyword(s):  
Abelian Group ◽  
Abelian Groups ◽  
Group Topology ◽  
Sequential Convergence ◽  
Hausdorff Group

Given an abelian groupGand a non-trivial sequence inG, when will it be possible to construct a Hausdroff topology onGthat allows the sequence to converge? As one might expect of such a naive question, the answer is far too complicated for a simple response. The purpose of this paper is to provide some insights to this question, especially for the integers, the rationals, and any abelian groups containing these groups as subgroups. We show that the sequence of squares in the integers cannot converge to0in any Hausdroff group topology. We demonstrate that any sequence in the rationals that satisfies a “sparseness” condition will converge to0in uncountably many different Hausdorff group topologies.

Dual properties in totally bounded Abelian groups

2003 ◽  
Vol 80 (3) ◽  
pp. 271-283 ◽  
Author(s):  
S. Hernández ◽  
S. Macario
Keyword(s):  
Abelian Groups ◽  
Totally Bounded
Sign in / Sign up

Export Citation Format

Share Document