Definition:Closure

Disambiguation

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Closure may refer to:

• 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 $R$.