# Open cone homeomorphic to the Euclidean space

Let $$X$$ be a topological space and the open cone $$C(X)$$ over $$X$$ is defined to be $$X times (0,1)$$ with $$X times {0}$$ identified. Suppose $$C(X)$$ is homeomorphic to $$mathbb R^4$$, can we prove that $$X$$ is homeomorphic to $$S^3$$.