How would I prove the following containment relation about the interior of a union:
(A B)º Aº Bº
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.