‎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. پرونده مقاله

In this paper, we study some categorical structures of the category $\mathbf{CoarsePro}$, whose objects are coarse proximity spaces and whose morphisms are coarse proximity maps. We investigate the structure of initial, final, embedding and quotient morphisms in the construct $\mathbf{CoarsePro}$. A special attention is paid to investigate quotients by introducing some conditions that they exist. Also, it is shown that bimorphisms are exactly bijective coarse proximity maps, but not isomorphisms. Consequently, $\mathbf{CoarsePro}$ is not balanced. پرونده مقاله