/sci/ - Science & Math

Hey /sqt/bros it's me again with a question from Fomenko-Fuchs.
He says that homeomorphism between S^n/ (S^n - Ua) and S^n/(S^n - U) is a homeomorphism between two spheres. Although each space is homeomorphic to a sphere, isn't the induced homeomorphism of spheres dependent on which homeomorphism you choose? Or does he mean the homeomorphisms which are homotopic to the canonical projection maps S^n S^n/(S^n - U) and S^n S^n/ (S^n - Ua) ?