closure axioms
A closure operator on a set is an operator which assigns a set to each subset of , and such that the following (Kuratowski’s closure axioms) hold for any subsets and of :
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The following theorem due to Kuratowski says that a closure operator characterizes a unique topology on :
Theorem. Let be a closure operator on , and let . Then is a topology on , and is the -closure of for each subset of .
Title | closure axioms |
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Canonical name | ClosureAxioms |
Date of creation | 2013-03-22 13:13:44 |
Last modified on | 2013-03-22 13:13:44 |
Owner | Koro (127) |
Last modified by | Koro (127) |
Numerical id | 9 |
Author | Koro (127) |
Entry type | Definition |
Classification | msc 54A05 |
Synonym | Kuratowski’s closure axioms |
Synonym | Kuratowski closure axioms |
Related topic | Closure |
Defines | closure operator |