基于软拓扑空间软理想的同余表示

IF 1.9 3区 数学 Q1 MATHEMATICS, APPLIED Axioms Pub Date : 2023-10-28 DOI:10.3390/axioms12111015
Zanyar A. Ameen, Mesfer H. Alqahtani
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引用次数: 0

摘要

本文首先研究了软集合模软理想的同余性。利用软拓扑空间中不同类型的软理想引入新的软开集弱类。即软开集模无软密集和软开集模第一类软集。建立了这些类的基本属性和表示。一类软开集模软无处稠密集形成一个软代数。该软代数中的元主要是软集,其软边界是软无处稠密集。第一类软开集的模软集称为Baire性质的软集,是一个软的σ-代数。本文主要研究具有Baire性质的软集的软σ-代数。我们证明了具有Baire性质的软集可以用软拓扑空间中的各种自然类别的软集来表示。此外,我们还发现具有Baire性质的软集的软σ-代数包含了软Borel σ-代数。进一步证明了在某一软拓扑中具有Baire性质的软集等于由原拓扑构成的聚类软拓扑中的软Borel集。
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Congruence Representations via Soft Ideals in Soft Topological Spaces
This article starts with a study of the congruence of soft sets modulo soft ideals. Different types of soft ideals in soft topological spaces are used to introduce new weak classes of soft open sets. Namely, soft open sets modulo soft nowhere dense sets and soft open sets modulo soft sets of the first category. The basic properties and representations of these classes are established. The class of soft open sets modulo the soft nowhere dense sets forms a soft algebra. Elements in this soft algebra are primarily the soft sets whose soft boundaries are soft nowhere dense sets. The class of soft open sets modulo soft sets of the first category, known as soft sets of the Baire property, is a soft σ-algebra. In this work, we mainly focus on the soft σ-algebra of soft sets with the Baire property. We show that soft sets with the Baire property can be represented in terms of various natural classes of soft sets in soft topological spaces. In addition, we see that the soft σ-algebra of soft sets with the Baire property includes the soft Borel σ-algebra. We further show that soft sets with the Baire property in a certain soft topology are equal to soft Borel sets in the cluster soft topology formed by the original one.
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来源期刊
Axioms
Axioms Mathematics-Algebra and Number Theory
自引率
10.00%
发文量
604
审稿时长
11 weeks
期刊介绍: Axiomatic theories in physics and in mathematics (for example, axiomatic theory of thermodynamics, and also either the axiomatic classical set theory or the axiomatic fuzzy set theory) Axiomatization, axiomatic methods, theorems, mathematical proofs Algebraic structures, field theory, group theory, topology, vector spaces Mathematical analysis Mathematical physics Mathematical logic, and non-classical logics, such as fuzzy logic, modal logic, non-monotonic logic. etc. Classical and fuzzy set theories Number theory Systems theory Classical measures, fuzzy measures, representation theory, and probability theory Graph theory Information theory Entropy Symmetry Differential equations and dynamical systems Relativity and quantum theories Mathematical chemistry Automata theory Mathematical problems of artificial intelligence Complex networks from a mathematical viewpoint Reasoning under uncertainty Interdisciplinary applications of mathematical theory.
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