**Mayer-Vietoris Sequence**

For a pair of subspaces such that , the exact MV sequence has the form

**Example: **

Let with and the northern and southern hemispheres, so that . Then in the reduced Mayer-Vietoris sequence the terms are zero. So from the reduced Mayer-Vietoris sequence we get the exact sequence

We obtain isomorphisms .

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