normal
A topological space is said to be normal if is (i.e. singletons are closed), and for all disjoint closed sets there exist disjoint open sets and such that and (i.e, is also ).
Some authors do not require the axiom as part of this definition.
Title | normal |
Canonical name | Normal |
Date of creation | 2013-03-22 12:12:39 |
Last modified on | 2013-03-22 12:12:39 |
Owner | Koro (127) |
Last modified by | Koro (127) |
Numerical id | 14 |
Author | Koro (127) |
Entry type | Definition |
Classification | msc 54D15 |
Synonym | normality |
Synonym | normal |
Related topic | SeparationAxioms |
Related topic | Tychonoff |
Related topic | Hausdorff |
Related topic | CompletelyNormal |
Related topic | T2Space |
Related topic | AConnectedNormalSpaceWithMoreThanOnePointIsUncountable2 |
Related topic | AConnectedNormalSpaceWithMoreThanOnePointIsUncountable |
Related topic | ApplicationsOfUrysohnsLemmaToLocallyCompactHausdorffSpaces |