The simplification of axiomatical systems of lattice topology
Jiangong Wang · Journal of Northwest University · 2004
AimTo simplify the axiomatical system of the pan-neighbourhood system and the net pan-convergence relation. MethodsTo build up the basic conditions of the pan-neighborhood system and the net pan-convergence relation of lattice topology against the axiomatical theory of the neighbourhood system and the theory of the More-smith convergence of general topologies. Results The seven axioms on the pan-neighborhood system and the eight axioms on the net pan-convergence relation are simplified to the five axioms respectively. Conclusion After the axiomatical system of the pan-neighbourhood system and the net pan-convergence are simplified,a clearer demonstration and a more convenient appliance will be shown.