scholarly journals Arcs in the Pontryagin dual of a topological abelian group

2015 ◽  
Vol 425 (1) ◽  
pp. 337-348 ◽  
Author(s):  
L. Außenhofer ◽  
M.J. Chasco ◽  
X. Domínguez
Keyword(s):  
Abelian Group ◽  
Topological Abelian Group

scholarly journals Duality for topological abelian group stacks and T-duality

2009 ◽  
pp. 227-347 ◽  
Author(s):  
Ulrich Bunke ◽  
Thomas Schick ◽  
Markus Spitzweck ◽  
Andreas Thom
Keyword(s):  
Abelian Group ◽  
Topological Abelian Group

Čech Cohomology with Coefficients in a Topological Abelian Group

2015 ◽  
Vol 211 (1) ◽  
pp. 40-57
Author(s):  
L. Mdzinarishvili ◽  
L. Chechelashvili
Keyword(s):  
Abelian Group ◽  
Topological Abelian Group ◽  
Cech Cohomology

scholarly journals Commutative Topological Semigroups Embedded into Topological Abelian Groups

Axioms ◽  
2020 ◽  
Vol 9 (3) ◽  
pp. 87
Author(s):  
Julio César Hernández Arzusa
Keyword(s):  
Topological Group ◽  
Abelian Group ◽  
Topological Semigroup ◽  
Abelian Groups ◽  
Sufficient Conditions ◽  
Locally Compact ◽  
Topological Abelian Group ◽  
Topological Semigroups ◽  
Topological Monoid

In this paper, we give conditions under which a commutative topological semigroup can be embedded algebraically and topologically into a compact topological Abelian group. We prove that every feebly compact regular first countable cancellative commutative topological semigroup with open shifts is a topological group, as well as every connected locally compact Hausdorff cancellative commutative topological monoid with open shifts. Finally, we use these results to give sufficient conditions on a commutative topological semigroup that guarantee it to have countable cellularity.

scholarly journals A Locally Compact Non Divisible Abelian Group Whose Character Group Is Torsion Free and Divisible

2013 ◽  
Vol 56 (1) ◽  
pp. 213-217 ◽  
Author(s):  
Daniel V. Tausk
Keyword(s):  
Abelian Group ◽  
Locally Compact ◽  
Topological Abelian Group ◽  
Character Group ◽  
Divisible Abelian Group ◽  
Torsion Free

AbstractIt was claimed by Halmos in 1944 that if G is a Hausdorff locally compact topological abelian group and if the character group of G is torsion free, then G is divisible. We prove that such a claim is false by presenting a family of counterexamples. While other counterexamples are known, we also present a family of stronger counterexamples, showing that even if one assumes that the character group of G is both torsion free and divisible, it does not follow that G is divisible.

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