Abstract:  In this paper，we investigate some special properties of lattice implication homomorphism in implication filter spaces．We show that lattice implication homomorphism is a continuous function with respect to implication filter topology．Moreover，we give a structural characterstic of left-translation topology and right-translation topology，which finally leads to the structural characteristics of product topology．

Key words: lattice implication homomorphism, implication filter spaces, implication filter topology