Topologies, posets and finite quandles

• M. Elhamdadi ^[1] ; T. Gona ^[2] ; H. Lahrani ^[1]
  1. [1] Department of Mathematics and Statistics, University of South FloridaTampa, FL33620, U.S.A
  2. [2] Department of Mathematics, University of California Berkeley, CA94720, U.S.A.
• Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 38, Nº 1, 2023, págs. 1-15
• Idioma: inglés
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• Resumen

  • An Alexandroff space is a topological space in which every intersection of open sets isopen. There is one to one correspondence between AlexandroffT0-spaces andpartially ordered sets(posets). We investigate AlexandroffT0-topologies on finite quandles. We prove that there is anon-trivial topology on a finite quandle making right multiplications continuous functions if andonly if the quandle has more than one orbit. Furthermore, we show that right continuous posets onquandles withnorbits aren-partite. We also find, for the even dihedral quandles, the number ofall possible topologies making the right multiplications continuous. Some explicit computations forquandles of cardinality up tofiveare given