Open Set

A Set is open if every point in the set has a Neighborhood lying in the set. An open set of Radius and center is the set of all points such that , and is denoted . In 1-space, the open set is an Open Interval. In 2-space, the open set is a Disk. In 3-space, theopen set is a Ball.

More generally, given a Topology (consisting of a Set and a collection of Subsets), a Set is said to be open if it is in . Therefore, while it is not possible for a set to be both finiteand open in the Topology of the Real Line (a single point is a Closed Set), it is possible for amore general topological Set to be both finite and open.

The complement of an open set is a Closed Set. It is possible for a set to be neither open nor Closed, e.g., the interval .

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