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 .

• Banzhaf Power Index
• Barber Paradox
• Barbier's Theorem
• Bare Angle Center
• Bar (Edge)
• Barnes G-Function
• Barnes' Lemma
• Barnes-Wall Lattice
• Barnsley's Fern
• Bar Polyhex
• Bar Polyiamond
• Barrier
• Barth Decic
• Barth Sextic
• Bartlett Function
• Barycentric Coordinates
• Baseball
• Baseball Cover
• Base Curve
• Base (Logarithm)
• Base (Neighborhood System)
• Base (Number)
• Base Space
• Basin of Attraction
• Basis