Penggunaan Teorema Homeomorphy 2-Manifold dan Teorema Euler Poincare pada Torus 𝑇�� dan Simplicial Complex 𝐾��

Abstract

Two dimensional topological spaces are said to be homeomorphic if they have the same topological invariant, where one of topological invariant used is an Euler characteristic. Homeomorphy 2-Manifold’s Theorem and Euler Poincare’s Theorem are used to distinguish two topological spaces. Homeomorphy 2-Manifold’s Theorem uses Euler characteristic to identify two dimensional topological spaces. Euler Poincare’s Theorem is an alternative way to find Euler characteristic with Betti number, which is topological invariant as well. The objective of this paper is to investigate the homeomorphism of torus 𝑇����� and simplicial complex 𝐾�����. Topological space torus and simplicial complex 𝐾����� have the same Euler characteristic, which is two. Based on Homeomorphy 2-Manifold’s Theorem topological space torus 𝑇����� and simplicial complex 𝐾����� is homeomorphic.