Let X and Y be compact metric spaces. Let S ( X , Y ) S(X,Y) denote the collection of standard maps of X onto Y . We establish that S ( C , Y ) S(C,Y) is a dense subset of C ( C , Y ) C(C,Y) , where C is the Cantor set. If f is a standard map and G ( f , Y ) { A ( f , Y ) } G(f,Y)\{ A(f,Y)\} denotes the subgroup of H ( X ) H(X) which preserves {interchanges} the point-inverses of f , then there is a continuous homomorphism of A ( f , Y ) A(f,Y) into H ( Y ) H(Y) with kernel G ( f , Y ) G(f,Y) . We also show that G ( f , Y ) G(f,Y) and A ( f , Y ) A(f,Y) are closed subsets of H ( X ) H(X) .