The Topological Quandles up to Four Elements

Abstract

The finite topological quandles can be represented as $n\times n$ matrices, recently defined by S. Nelson and C. Wong. 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.