Proximity spaces via hereditary classes
الموضوعات :
1 - Department of Mathematics and Computer Sciences, Sirjan University of Technology, Sirjan, Iran
الکلمات المفتاحية: Generalized topology, H-proximity space, Hereditary class,
ملخص المقالة :
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.
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