  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.
