Hatcher, *Algebraic Topology*, Chapter 0

**23. Show that a CW complex is contractible if it is the union of two contractible subcomplexes whose intersection is also contractible.**

*Proof.* Let be the union of CW complexes and which are contractible and for which is contractible. Contract the intersection to get the wedge of the complexes and . Both of these are contractible (details).

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