Results 41 to 50 of about 80,484 (161)

On topological groups with a weak q-point

Applied General Topology
In this article, firstly, we introduce the concepts of weak q-spaces and weak sq-spaces. Some properties of these spaces are discussed. Secondly, we study weak q-spaces and weak sq-spaces in topological groups in terms of preimages of submetrizable ...
Hai-Hua Lin, Li-Hong Xie
doaj   +1 more source

On topological groups via a-local functions

Applied General Topology, 2014
An ideal on a set X is a nonempty collection of subsets of X which satisfies the following conditions (1)A ∈ I and B ⊂ A implies B ∈ I; (2) A ∈ I and B ∈ I implies A ∪ B ∈ I. Given a topological space (X; ) an ideal I on X and A ⊂ X, ℜa(A) is defined as ∪
Wadei Al-Omeri, M. Salmi Md. Noorani, A. Al-Omari   +2 more
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Weak Convergence of Robust Functions on Topological Groups

Mathematics
This paper introduces weak variants of level convergence (L-convergence) and epigraph convergence (E-convergence) for nets of level functions on general topological spaces, extending the classical metric and real-valued frameworks to ordered codomains ...
Víctor Ayala, Heriberto Román-Flores, Adriano Da Silva   +2 more
doaj   +1 more source

Eilenberg–Mac Lane Spaces for Topological Groups

Axioms, 2019
In this paper, we establish a topological version of the notion of an Eilenberg−Mac Lane space. If X is a pointed topological space, π 1 ( X ) has a natural topology coming from the compact-open topology on the space of maps S
Ged Corob Cook
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Properties of locally semi-compact Ir-topological groups

Open Mathematics, 2023
This study investigates some topological properties of locally semi-compact Ir-topological groups and establishes the relationship between Ir-topological groups and semi-compact spaces.
Wang ZhongLi, Teh Wen Chean
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SOME NEW CONCEPTS IN TOPOLOGICAL GROUPS

Journal of New Theory, 2016
Abstaract−In this study, we define a new boundedness concept different from existing definitions. Also we give some theorems and results in topological groups.
Demet Binbaşıoğlu, İlhan İçen, - Yılmaz   +2 more
doaj  

Convergent nets in abelian topological groups

International Journal of Mathematics and Mathematical Sciences, 2001
A net in an abelian group is called a T-net if there exists a Hausdorff group topology in which the net converges to 0. This paper describes a fundamental system for the finest group topology in which the net converges to 0.
Robert Ledet
doaj   +1 more source

Topological groups with dense compactly generated subgroups

Applied General Topology, 2002
A topological group G is: (i) compactly generated if it contains a compact subset algebraically generating G, (ii) -compact if G is a union of countably many compact subsets, (iii) 0-bounded if arbitrary neighborhood U of the identity element of G has ...
Hiroshi Fujita, Dimitri Shakhmatov
doaj   +1 more source

Unitary representability of free abelian topological groups

Applied General Topology, 2008
For every Tikhonov space X the free abelian topological group A(X) and the free locally convex vector space L(X) admit a topologically faithful unitary representation. For compact spaces X this is due to Jorge Galindo.
Vladimir V. Uspenskij
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The character of free topological groups I

Applied General Topology, 2005
A systematic analysis is made of the character of the free and free abelian topological groups on uniform spaces and on topological spaces. In the case of the free abelian topological group on a uniform space, expressions are given for the character in ...
Peter Nickolas, Mikhail Tkachenko
doaj   +1 more source