**Closure (topology)**

In mathematics, the **closure** of a subset *S* in a topological space consists of all points in *S* plus the limit points of *S*. Intuitively, these are all the points that are "near" *S*. A point which is in the closure of *S* is a point of closure of *S*. The notion of closure is in many ways dual to the notion of interior.

Read more about Closure (topology): Examples, Closure Operator, Facts About Closures, Categorical Interpretation

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Closure (topology) - Categorical Interpretation

... One may elegantly define the

... One may elegantly define the

**closure**operator in terms of universal arrows, as follows ... Furthermore, a**topology**T on X is a subcategory of P with inclusion functor ... All properties of the**closure**can be derived from this definition and a few properties of the above categories ...Main Site Subjects

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