| Abstract: | Abstract Let (Z,Γ) be an H-structure. Then, for each exponential object Y in TOP, an H-structure is induced on the topological space Ct(Y,Z) of continuous maps equipped with the appropriate function space topology t (e.g. t = Tis, where Tis is the Isbell topology on C(Y,Z)). If (Z,Γ) is H-associative (resp.admits inversion), then the induced H-structure is also H-associative (resp. admits inversion). If (Z,Γ) is H-associative and admits inversion (e.g. a topological group) then all path components of Ct(Y,Z) belong to the same homotopy type. We also study the special case of (Z,Γ) being a topological group. Moreover, we prove that certain functions between function spaces are H-homomorphisms of the induced H-structures in the function spaces. |
