•Journal•ISSN: 2299-3231
Topological Algebra and its Applications
De Gruyter Open
About: Topological Algebra and its Applications is an academic journal published by De Gruyter Open. The journal publishes majorly in the area(s): Computer science & Metric space. It has an ISSN identifier of 2299-3231. It is also open access. Over the lifetime, 93 publications have been published receiving 290 citations.
Topics: Computer science, Metric space, Fixed point, Internal medicine, Monoid
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TL;DR: In this article, it was shown that a regular totally ω-narrow paratopological group G has countable index of regularity, i.e., for every neighborhood U of the identity e of G, we can find a neighborhood V of e and a countable family of neighborhoods of e in G such that ∩W∈γ VW−1⊆ U.
Abstract: Abstract We show that a regular totally ω-narrow paratopological group G has countable index of regularity, i.e., for every neighborhood U of the identity e of G, we can find a neighborhood V of e and a countable family of neighborhoods of e in G such that ∩W∈γ VW−1⊆ U. We prove that every regular (Hausdorff) totally !-narrow paratopological group is completely regular (functionally Hausdorff). We show that the index of regularity of a regular paratopological group is less than or equal to the weak Lindelöf number. We also prove that every Hausdorff paratopological group with countable π- character has a regular Gσ-diagonal.
29 citations
TL;DR: In this paper, it was shown that every idempotent weakly divisible residuated lattice satisfying the double negation law can be transformed into an orthomodular lattice.
Abstract: Abstract We show that every idempotent weakly divisible residuated lattice satisfying the double negation law can be transformed into an orthomodular lattice. The converse holds if adjointness is replaced by conditional adjointness. Moreover, we show that every positive right residuated lattice satisfying the double negation law and two further simple identities can be converted into an orthomodular lattice. In this case, also the converse statement is true and the corresponence is nearly one-to-one.
20 citations
TL;DR: The concept of topological rough groups as discussed by the authors is a simple combination of the concepts of abstract group and topological space, which was introduced in the context of topology space and rough groups.
Abstract: 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.
16 citations
TL;DR: In this paper, it was shown that Protasov's theorem on non-closed discrete subsets of precompact topological groups cannot be extended to paratopological groups.
Abstract: Abstract We construct a precompact completely regular paratopological Abelian group G of size (2ω)+ such that all subsets of G of cardinality ≤ 2ω are closed. This shows that Protasov’s theorem on non-closed discrete subsets of precompact topological groups cannot be extended to paratopological groups. We also prove that the group reflection of the product of an arbitrary family of paratopological (even semitopological) groups is topologically isomorphic to the product of the group reflections of the factors, and that the group reflection, H*, of a dense subgroup G of a paratopological group G is topologically isomorphic to a subgroup of G*.
12 citations
TL;DR: In this article, it was shown that the topological entropy of a semigroup action on a totally disconnected locally compact abelian group coincides with the algebraic entropy of the dual action, and this relation holds both for the entropy relative to a net and for the receptive entropy of finitely generated monoid actions.
Abstract: Abstract The topological entropy of a semigroup action on a totally disconnected locally compact abelian group coincides with the algebraic entropy of the dual action. This relation holds both for the entropy relative to a net and for the receptive entropy of finitely generated monoid actions.
11 citations