In this presentation, I will explain the results obtained in my paper entitled "The Topological Whenles up to Four Elements", In this paper, we first study the finite topological quandles and we show how to use these matrices to distinguish all isomorphism classes of finite topological quandles for a given cardinality n. As an application, we classify finite topological quandles with up to 4 elements. Furthermore, I will explain the results obtained in my paper in collaboration with Dominique Manchon entitled " A twisted Hopf algebra of finite topological quandles", In this paper, we construct two twisted bialgebra structures on this species, one of the first kind and one of the second kind. The obstruction for the structure to match the double twisted bialgebra axioms is explicitly described.
