Some Notes on L-Semi Topological Space

Firstly, the concepts of both Left-semi topology and Right-semi topology are introduced by means of both sup-semi-topology and inf-semi-topology. Then, the point set theory of Left-semi-topological (i.e., L-semi-topological) spaces is discussed. Some results on basic point sets, the properties of subspaces and the convergence of the net are obtained on L-semi-topological spaces. Furthermore, some basic properties of topological spaces are generalized, and it is cited by counterexamples that some results are not true on a L-semi topological space, but they are correct on topological spaces.