Topological Algebra and its Applications

Open Access Published by De Gruyter Open Access

Volume 4 Issue 1

January 2016

Issue of Topological Algebra and its Applications

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Contents
Journal Overview

Open Access April 15, 2016

On the Bézout equation in the ring of periodic distributions

Rudolf Rupp, Amol Sasane

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Abstract

A corona type theorem is given for the ring D'A(Rd) of periodic distributions in Rd in terms of the sequence of Fourier coefficients of these distributions,which have at most polynomial growth. It is also shown that the Bass stable rank and the topological stable rank of D'A(Rd) are both equal to 1.

Open Access August 1, 2016

Quotients of Strongly Realcompact Groups

L. Morales, M. Tkachenko

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Abstract

A topological group is strongly realcompact if it is topologically isomorphic to a closed subgroup of a product of separable metrizable groups. We show that if H is an invariant Čech-complete subgroup of an ω-narrow topological group G, then G is strongly realcompact if and only if G/H is strongly realcompact. Our proof of this result is based on a thorough study of the interaction between the P-modification of topological groups and the operation of taking quotient groups.

Open Access October 7, 2016

On unitary extensions and unitary completions of topological monoids

Boris G. Averbukh

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Abstract

The concept of a unitary Cauchy net in an arbitrary Hausdorff topological monoid generalizes the concept of a fundamental sequence of reals. We construct extensions of this monoid where all its unitary Cauchy nets converge.

Open Access December 30, 2016

Topological Rough Groups

Nurettin Bağırmaz, İlhan İçen, Abdullah F. Özcan

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Abstract

The concept of topological group is a simple combination of the concepts of abstract group and topological space. The purpose of this paper is to combine the concepts of topological space and rough groups; called topological rough groups on an approximation space.

About this journal

The area of topological algebra and its applications is recently enjoying very fast development, with a great number of specialized conferences. Topological Algebra and its Applications is a fully peer-reviewed open access electronic journal that publishes original research articles on topological-algebraic structures. This journal is devoted to the publication of original high quality research papers of moderate length in all fields of the subject. The highest standards of contents of Topological Algebra and its Applications are guaranteed by members of the Editorial Advisory Board and invited external referees, all of them selected from the world prominent experts in this field.

Why subscribe and read

Topological Algebra and its Applications publishes original research articles on topological-algebraic structures, namely:

Topological *-algebras,
C*-algebras,
(para)topological groups,
Topological semigroups,
Semigroups of operators,
Fuzzy topological algebras,
Hilbert C*-modulus,
Function spaces etc.,

and their applications to (abstract) topological dynamics, noncommutative probability, etc.

The journal also intends to disseminate results on applications of these structures to physics, computer science, economy, as well as other areas of mathematics.
Besides research papers, we publish short notes, surveys and issues focused on themes of current interest.