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مقاله
1 - Proximity spaces via hereditary classesJournal of Linear and Topological Algebra , شماره 5 , سال 11 , پاییز 2022A 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 چکیده کاملA 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 -
مقاله
2 - Some categorical aspects of coarse proximity spacesJournal of Linear and Topological Algebra , شماره 1 , سال 13 , زمستان 2024In 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 con چکیده کاملIn 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