Hello;

Let M be a manifold and let U be a nonempty euclidean open subset of M. Let B be a nonempty open ball whose compact closure cl(B) is contained in U. Let H(cl(B)) be the group of homeomorphisms of cl(B). Then prove that the set of all functions in H(cl(B)) that fix the boundary ∂B of B pointwise is not compact.

Kindly guide me and every guidance is highly appreciated.

Thank you very much