Interpretation of Weil’s Theorem

This is an introductory paper based on general knowledge such as simplicial complex, nerves and their homotopy equivalents in the topology field. It focuses on the theoretical part of one of the four statements on nerve theorem of paper variations on the nerve theorem. One of many ideologies throughout this theorem is to conduct an approximating process on mathematical spaces with restrictions, which is the bridge from a theory to an application of Weil’s theorem and many others. Besides, work done by Kathryn Heal in her paper variations on the nerve theorem has proved the correctness and feasibility about Weil’s theorem. This paper aims to clarify her proof of Weil’s theorem and make it more easier for people to understand.