On the Structure of Hopf Algebras

In this paper we present the construction of a group Hopf algebra on the class of rational tangles.A locally finite partial order on this class is introduced and a topology is generated.An interval coalgebra structure associated with the locally finite partial order is specified.Irrational and real tangles are introduced and their relation with rational tangles are studied.The existence of the maximal real tangle is described in detail.