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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