A subset A of T is open in T if for all x in A there is an open neighborhood in A centered at x.

A member of a class of subsets of a topological space that satisfy certain axioms and define the topology.

An open set is a member of the topology.

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.