Let $$Y$$ be a subspace of $$X$$. The wizard hat space $$W$$ is constructed by attaching the base of the cone $$CY$$ over $$Y$$ to $$X$$ along $$Y$$.

(This showed up in a topology class I took once. We needed to use the fact that $$W$$ deformation retracts onto $$X$$, but I don't remember what it was used for. The name is mine.)

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