[Math] Mayer-Vietoris of pair (X,C)

algebraic-topologyhomology-cohomology

I would like to know if i can use Mayer-Vietoris with this form:

Let X be a topological space and A, B be two subspaces whose interiors cover X and $C\subset A\cap B$.

We get the exact sequence

$… \rightarrow H_q(A\cap B,C)\rightarrow H_q(A,C)\oplus H_q(B,C)\rightarrow H_q(X,C) \rightarrow …$

It is true? i am trying to solve a problem of homology groups and i get stuck, and if this is true that could help me solve it, i would appreciate any comment

Best Answer

Yes, take $C = D = Y$ here:

http://en.wikipedia.org/wiki/Mayer%E2%80%93Vietoris_sequence#Relative_form

For a proof, see p. 152 of Hatcher's Algebraic Topology.

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