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The word neighborhood is a word with many different levels of meaning in mathematics. One of the most general concepts of a neighborhood of a point $x\in\Bbb{R}^n$ (also called an Epsilon-Neighborhood or infinitesimal Open Set) is the set of points inside an $n$-Ball with center $x$ and Radius $\epsilon>0$.

© 1996-9 Eric W. Weisstein