Here's one way to go about it. Pick an arbitrary Then, WLOG, This implies that there is an such that an open ball centered at of radius is contained in Now show that both and the ball is also contained in That should do it, right?
You can call it a neighborhood, or a sphere, or whatever you want. On the real line, it'd be an open interval of length centered at In 2 dimensions, it'd be a circle of radius centered at (using the usual Euclidean length). In 3D, it'd be a sphere of radius centered at the vector And so on. Does that make sense? It's a small open set containing That's the critical part.