Topological Spaces

Definition 1   A Closed Set is a set whose complement is Open.

Remember that a Topology is nothing more or less than a definition of Open Sets. These may or may not look anything like Open Intervals in the Real Numbers.

Definition 2   Given a set a in a space , and a point , x is a Limit Point of iff every open set containing x has a non-empty intersection with .

Proposition 1   A set is closed iff it contains all its limit points.