Resumen de Topologies, posets and finite quandles

M. Elhamdadi, T. Gona, H. Lahrani

• 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