Homeomorphism between Finite Topological Spaces, Two-Dimensional Lattice Spaces and a Fixed Point Theorem

Summary. In this paper we first introduced the notion of homeomorphism between finite topological spaces. We also gave a fixed point theorem in finite topological space. Next, we showed two 2-dimensional concrete models of lattice spaces. One was 2-dimensional linear finite topological space. Another was 2dimensional small finite topological space.