Some categorical aspects of coarse proximity spaces

Subject Areas : General topology

Gh.  Mirhosseinkhani ¹ (Department of Mathematics, Sirjan University of technology)

Received: 2023-10-21 Accepted : 2024-03-10 Published : 2024-03-07

Keywords: Coarse proximity space, coarse proximity category, embedding morphism, quotient morphism, bimorphism,

Abstract :

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.

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