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arXiv · 2209.14518

Topologies, Posets and Finite Quandles

Mohamed Elhamdadi·Tushar Gona·Hitakshi Lahrani
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Abstract

An Alexandroff space is a topological space in which every intersection of open sets is open. There is one to one correspondence between Alexandroff $T_0$-spaces and partially ordered sets (posets). We investigate Alexandroff $T_0$-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.

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Mohamed Elhamdadi, Tushar Gona, Hitakshi Lahrani. 2022-09-29. Topologies, Posets and Finite Quandles. https://arxiv.org/abs/2209.14518

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