Closure

A Set and a Binary Operator are said to exhibit closure if applyingthe Binary Operator to two elements returns a value which is itself a member of .

The term ``closure'' is also used to refer to a ``closed'' version of a given set. The closure of a Set can be definedin several equivalent ways, including

1. The Set plus its Limit Points, also called ``boundary'' points, the union ofwhich is also called the ``frontier,''

2. The unique smallest Closed Set containing the given Set,

3. The Complement of the interior of the Complement of the set,

4. The collection of all points such that every Neighborhood of them intersects the original Set in anonempty Set.

• Area-Preserving Map
• Area Principle
• Arf Invariant
• Argand Diagram
• Argand Plane
• Argoh's Conjecture
• Argument Addition Relation
• Argument (Complex Number)
• Argument (Elliptic Integral)
• Argument (Function)
• Argument Multiplication Relation
• Argument Principle
• Argument Variation
• Aristotle's Wheel Paradox
• Arithmetic
• Arithmetic-Geometric Mean
• Arithmetic Geometry
• Arithmetic-Harmonic Mean
• Arithmetic-Logarithmic-Geometric Mean Inequality
• Arithmetic Mean
• Arithmetic Progression
• Arithmetic Sequence
• Arithmetic Series
• Armstrong Number
• Arnold Diffusion