a neighborhood of all its points

a neighborhood of any of its subsets

A set that is an element of a topology Ï„ defined on a set . Proof by Contradiction[ edit

A set is open if it is a member of the topology.

In topology and related fields of mathematics, a set U is called open if, intuitively speaking, you can "wiggle" or "change" any point x in U by a small amount in any direction and still be inside U. In other words, if x is surrounded only by elements of U; it can't be on the edge of U.