Consider a subspace X of ℝⁿ defined by polynomial equations. Suppose we fix a point p on X. When the implicit function theorem applies at p, the answer to the question in the title becomes clear! However, what happens when p is singular? A classical result ensures that X is locally topologically conical: for every sufficiently small ε > 0, the intersection of X with the ball of radius ε around p is homeomorphic to the cone formed over the intersection of X with the boundary sphere. Nevertheless, X is generally not metrically conical: there are parts of it which shrink faster than linearly when ε tends to 0. A natural problem is then to build classifications of the germs up to local bi-Lipschitz homeomorphism. I will give an introductive talk on this very active topic at the crossing point between metric topology and algebraic geometry.