There are several equivalent definitions of a closed Set. A Set is closed if

- 1. The Complement of is an Open Set,
- 2. is its own Closure,
- 3. Sequences/nets/filters in which converge do so within ,
- 4. Every point outside has a Neighborhood disjoint from .

The Point-Set Topological definition of a closed set is a set which contains all of its Limit Points. Therefore, a closed set is one for which, whatever point is picked outside of , can always be isolated in some Open Set which doesn't touch .

© 1996-9

1999-05-26