Hatcher, *Algebraic Topology*, Chapter 0

**21. If is a connected Hausdorff space that is a union of a finite number of 2-spheres, any two of which intersect in at most one point, show that is homotopy equivalent to a wedge sum of ‘s and ‘s.**

*Proof.* This follows immediately by induction on the procedure outlined in Example 0.9 of Hatcher’s book (pg 12), which makes use of the diagram in Figure 1 below.

**Figure 1**

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