Simply connected not implies contractible

This article gives the statement and possibly, proof, of a non-implication relation between two topological space properties. That is, it states that every topological space satisfying the first topological space property (i.e., Simply connected space (?)) need not satisfy the second topological space property (i.e., Contractible space (?))
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Statement

It is possible for a topological space to be a simply connected space but not a contractible space.

Related facts

• Simply connected not implies weakly contractible
• Weakly contractible not implies contractible

Proof

Example of spheres

All the spheres $S^{n},n\geq 2$, are simply connected spaces that are not contractible spaces.