Mayer–Vietoris Sequence

A long exact sequence in algebraic topology that relates the homology or cohomology of a space decomposed as the union of two subspaces A and B to the homology or cohomology of A, B, and their intersection A∩B, enabling computations via excision and algebraic gluing.

An exact long sequence in homology or cohomology derived from a cover of an object by two subobjects, relating the invariants of the whole to those of the parts and their intersection and enabling computations by patching local data.