Difference between revisions of "Normal topological space"
From Maths
(Creating skeleton.) |
m |
||
| (2 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
==[[Normal topological space/Definition|Definition]]== | ==[[Normal topological space/Definition|Definition]]== | ||
{{:Normal topological space/Definition}} | {{:Normal topological space/Definition}} | ||
| + | ==Equivalent statements== | ||
| + | * [[A topological space is normal if and only if for each closed set, E, and each open set, W, containing E there exists an open set U containing E such that the closure of U is strictly a subset of W]] | ||
| + | {{Todo|Make that sentence easier to read}} | ||
==See also== | ==See also== | ||
* [[Topological separation axioms]] | * [[Topological separation axioms]] | ||
* [[Regular topological space]] | * [[Regular topological space]] | ||
| + | * [[Urysohn's lemma]] | ||
| + | * [[Tietze extension theorem]] | ||
==References== | ==References== | ||
<references/> | <references/> | ||
{{Topology navbox|plain}} | {{Topology navbox|plain}} | ||
{{Definition|Topology}} | {{Definition|Topology}} | ||
Latest revision as of 00:14, 4 May 2016
Definition
A topological space, (X,J), is said to be normal if[1]:
- ∀E,F∈C(J) ∃U,V∈J[E∩F=∅⟹(U∩V=∅∧E⊆U∧F⊆V)] - (here C(J) denotes the collection of closed sets of the topology, J)
Equivalent statements
TODO: Make that sentence easier to read
See also
References
| |||||||||||||||||||||||
