Definition:Closure


 * Closure (Abstract Algebra): An algebraic structure $$\left({S, \circ}\right)$$ has the property of closure iff $$\forall \left({x, y}\right) \in S \times S: x \circ y \in S$$.


 * Closure (Topology): The closure of a subset $$A$$ of a topological space $$X$$ is the union of $$A$$ and its boundary.


 * Integral Closure (Commutative Algebra): The set of all elements of $A$ (where $A / R$ is a ring extension) that are integral over $R$.