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On pseudocompact topological Brandt λ 0 -extensions of semitopological monoids

Oleg Gutik, Kateryna Pavlyk (2013)

Topological Algebra and its Applications

In the paper we investigate topological properties of a topological Brandt λ0-extension B0λ(S) of a semitopological monoid S with zero. In particular we prove that for every Tychonoff pseudocompact (resp., Hausdorff countably compact, Hausdorff compact) semitopological monoid S with zero there exists a unique semiregular pseudocompact (resp., Hausdorff countably compact, Hausdorff compact) extension B0λ(S) of S and establish their Stone-Cˇ ech and Bohr compactifications. We also describe a category...

On rank one symmetric space

Inkang Kim (2004/2005)

Séminaire de théorie spectrale et géométrie

In this paper we survey some recent results on rank one symmetric space.

On regular endomorphism rings of topological Abelian groups

Horea Florian Abrudan (2011)

Czechoslovak Mathematical Journal

We extend a result of Rangaswamy about regularity of endomorphism rings of Abelian groups to arbitrary topological Abelian groups. Regularity of discrete quasi-injective modules over compact rings modulo radical is proved. A characterization of torsion LCA groups A for which End c ( A ) is regular is given.

On resolvable spaces and groups

Luis Miguel Villegas-Silva (1995)

Commentationes Mathematicae Universitatis Carolinae

It is proved that every uncountable ω -bounded group and every homogeneous space containing a convergent sequence are resolvable. We find some conditions for a topological group topology to be irresolvable and maximal.

On Riemann-Poisson Lie groups

Brahim Alioune, Mohamed Boucetta, Ahmed Sid’Ahmed Lessiad (2020)

Archivum Mathematicum

A Riemann-Poisson Lie group is a Lie group endowed with a left invariant Riemannian metric and a left invariant Poisson tensor which are compatible in the sense introduced in [4]. We study these Lie groups and we give a characterization of their Lie algebras. We give also a way of building these Lie algebras and we give the list of such Lie algebras up to dimension 5.

On Schwartz groups

L. Außenhofer, M. J. Chasco, X. Domínguez, V. Tarieladze (2007)

Studia Mathematica

We introduce a notion of a Schwartz group, which turns out to be coherent with the well known concept of a Schwartz topological vector space. We establish several basic properties of Schwartz groups and show that free topological Abelian groups, as well as free locally convex spaces, over hemicompact k-spaces are Schwartz groups. We also prove that every hemicompact k-space topological group, in particular the Pontryagin dual of a metrizable topological group, is a Schwartz group.

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