##  [Mayer–Vietoris Sequence](/mayer-vietoris-sequence-1) 

  ##  [Mayer–Vietoris Sequence](https://puremath.quantumdictionary.io/mayer-vietoris-sequence-2) 

  

 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

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.

 

 

 

 

 





 

 



 ##  [Mayer–Vietoris Sequence](https://algebra.quantumdictionary.io/mayer-vietoris-sequence-3) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

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.