closure
The closure of a subset of a topological space is the intersection of all closed sets containing .
Equivalently, consists of together with all limit points of in or equivalently if and only if every neighborhood of intersects . Sometimes the notation is used.
If it is not clear, which topological space is used, one writes . Note that if is a subspace of , then may not be the same as . For example, if , and , then while .
Title | closure |
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Canonical name | Closure |
Date of creation | 2013-03-22 12:05:40 |
Last modified on | 2013-03-22 12:05:40 |
Owner | mathwizard (128) |
Last modified by | mathwizard (128) |
Numerical id | 9 |
Author | mathwizard (128) |
Entry type | Definition |
Classification | msc 54A99 |
Related topic | ClosureAxioms |
Related topic | Interior |