Two Classes of Infrasoft Separation Axioms

One of the considerable topics in the soft setting is the study of soft topology which has enticed the attention of many researchers. To contribute to this scope, we devote this work to investigate two classes of separation axioms with respect to the distinct ordinary elements through one of the gen...

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Autores principales:	Tareq M. Al-shami, Jia-Bao Liu
Formato:	article
Lenguaje:	EN
Publicado:	Hindawi Limited 2021
Materias:	Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/40da0888739f496992a6807ac33d3c18
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spelling	oai:doaj.org-article:40da0888739f496992a6807ac33d3c182021-11-29T00:56:22ZTwo Classes of Infrasoft Separation Axioms2314-478510.1155/2021/4816893https://doaj.org/article/40da0888739f496992a6807ac33d3c182021-01-01T00:00:00Zhttp://dx.doi.org/10.1155/2021/4816893https://doaj.org/toc/2314-4785One of the considerable topics in the soft setting is the study of soft topology which has enticed the attention of many researchers. To contribute to this scope, we devote this work to investigate two classes of separation axioms with respect to the distinct ordinary elements through one of the generalizations of soft topology called infrasoft topology. We first formulate the concepts of infra-tp-soft Tj using total belong and partial nonbelong relations and then introduce the concepts of infra-tt-soft Tj-spaces using total belong and partial nonbelong relations. To illustrate the relationships between them, we provide some examples. We discuss their fundamental properties and study their behaviors under some special types of infrasoft topologies. An extensive discussion is given for the transmission of these two classes between infrasoft topology and its parametric infratopologies. In the end, we demonstrate which ones have topological and hereditary properties, and we show their behaviors under the finite product of soft spaces.Tareq M. Al-shamiJia-Bao LiuHindawi LimitedarticleMathematicsQA1-939ENJournal of Mathematics, Vol 2021 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Mathematics QA1-939
spellingShingle	Mathematics QA1-939 Tareq M. Al-shami Jia-Bao Liu Two Classes of Infrasoft Separation Axioms
description	One of the considerable topics in the soft setting is the study of soft topology which has enticed the attention of many researchers. To contribute to this scope, we devote this work to investigate two classes of separation axioms with respect to the distinct ordinary elements through one of the generalizations of soft topology called infrasoft topology. We first formulate the concepts of infra-tp-soft Tj using total belong and partial nonbelong relations and then introduce the concepts of infra-tt-soft Tj-spaces using total belong and partial nonbelong relations. To illustrate the relationships between them, we provide some examples. We discuss their fundamental properties and study their behaviors under some special types of infrasoft topologies. An extensive discussion is given for the transmission of these two classes between infrasoft topology and its parametric infratopologies. In the end, we demonstrate which ones have topological and hereditary properties, and we show their behaviors under the finite product of soft spaces.
format	article
author	Tareq M. Al-shami Jia-Bao Liu
author_facet	Tareq M. Al-shami Jia-Bao Liu
author_sort	Tareq M. Al-shami
title	Two Classes of Infrasoft Separation Axioms
title_short	Two Classes of Infrasoft Separation Axioms
title_full	Two Classes of Infrasoft Separation Axioms
title_fullStr	Two Classes of Infrasoft Separation Axioms
title_full_unstemmed	Two Classes of Infrasoft Separation Axioms
title_sort	two classes of infrasoft separation axioms
publisher	Hindawi Limited
publishDate	2021
url	https://doaj.org/article/40da0888739f496992a6807ac33d3c18
work_keys_str_mv	AT tareqmalshami twoclassesofinfrasoftseparationaxioms AT jiabaoliu twoclassesofinfrasoftseparationaxioms
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Two Classes of Infrasoft Separation Axioms

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