Topologies, posets and finite quandles

Authors

  • M. Elhamdadi Department of Mathematics and Statistics, University of South Florida Tampa, FL 33620, U.S.A.
  • H. Lahrani Department of Mathematics and Statistics, University of South Florida Tampa, FL 33620, U.S.A.
  • T. Gona Department of Mathematics, University of California Berkeley, CA 94720, U.S.A.

DOI:

https://doi.org/10.17398/2605-5686.38.1.1

Keywords:

quandles, topology, poset

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 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.

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Published

2023-06-01

Issue

Vol. 38 No. 1 (2023)

Section

Topology

How to Cite

Topologies, posets and finite quandles. (2023). Extracta Mathematicae, 38(1), 1-15. https://doi.org/10.17398/2605-5686.38.1.1