The neighborhood structures and convergence relations of the latlice topology had been established by Wang Peizhuang.The axiomatical desciptions in [1] can be simplified. In this paper, it gives the axiomatical systems of the neighborhood structures and convergence relations and proves it's independent property. As the axiomatical systems have been simplified, it is more simple and esay than [1] ,when we prove that the axiomatical descriptions on the neighborhood structures and convergence relations of the lattice topology is equivalent.
