Topologies, posets and finite quandles

An Alexandroff space is a topological in which every intersection of open sets open. There one to correspondence between T0 -spaces and partially ordered (posets). We investigate -topologies on finite quandles. prove that there non-trivial topology quandle making right multiplications continuous functions if only the has more than orbit. Furthermore, we show posets quandles with n orbits are n-partite. also find, for even dihedral quandles, number all possible topologies continuous. Some explicit computations cardinality up five given.