Proximity spaces via hereditary classes

Journal of Linear and Topological Algebra

دوره 11، شماره 04، اسفند 2022، صفحه 231-241   

نوع مقاله: Research Paper

شناسه دیجیتال (DOI): 10.30495/jlta.2022.698213

نویسنده

Gh. Mirhosseinkhani^*

Department of Mathematics and Computer Science‎s, ‎Sirjan University of Technology‎, ‎Sirjan‎, ‎Iran

چکیده

‎A hereditary class on a set $X$ is a nonempty collection of subsets of $X$ which is closed under‎ ‎subsets‎. ‎In this paper‎, ‎we present a new structure of proximity spaces by using a hereditary class‎, ‎called‎ ‎$\mathcal{H}$-proximity spaces‎, ‎as a generalization of Efremovi$\check{c}$ proximity spaces‎, ‎$I$-proximity spaces and‎ ‎coarse proximity spaces‎. ‎Some properties of this proximity structure and generalized topology induced by it are studied‎.
 

کلیدواژه‌ها

H-proximity space؛ Generalized topology؛ Hereditary class

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