2022/09/29 by Mohamed Elhamdadi, Elhamdadi, Mohamed, Tushar Gona +3
Computer Science · Mathematics · #54E99 #57K12 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #General Topology (math.GN) #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2209.14518
openalex publication_date 2022/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An Alexandroff space is a topological space in which every intersection of open sets is open. There is one to one correspondence between Alexandroff T0-spaces and partially ordered sets (posets). We investigate Alexandroff T0-topologies on finite quandles. We prove that there is a non-trivial topology on a finite quandle making right multiplications continuous functions if and only if the quandle has more than one orbit. Furthermore, we show that right continuous posets on quandles with n orbits are n-partite. We also find, for the even dihedral quandles, the number of all possible topologies making the right multiplications continuous. Some explicit computations for quandles of cardinality up to five are given.