Real Analysis/Open and Closed Sets

Terminology

The open ball in a metric space (X,d) with radius \epsilon centered at a, is denoted B(a, \epsilon) . Formally B(a, \epsilon) = \{x \in X: d(a,x) < \epsilon\}

Definition

Let (X,d) be a metric space. We say a set A \subset X is open if for every x \in A \text{ } \exists \epsilon > 0 such that B(x,\epsilon) \subset A .

We say a set B \subset X is closed if X\backslash B is open.

Last modified on 28 November 2009, at 14:18