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## Main Question or Discussion Point

I'm a bit confused about the idea of contractible spaces. These spaces are homotopy equivalent to a single-point space {0}. As far as I can see, a space is contractible if and only if it is path connected. However, wikipedia states that a contractible space must also be simply connected. Isn't the punctured disc contractible? Every point is path connected to every other point, so it should be simple to create a homotopy equivalence.