Mayer—Vietoris

Abstract

For open sets U and V in the plane (or any topological space) we will define a homomorphism

$$ \partial :{{H}_{1}}\left( {U \cup V} \right) \to {{H}_{0}}\left( {U \cap V} \right), $$

called the boundary map.⁵ To do this we need a lemma.