completely Hausdorff
Definition 1.
[1]
Let be a topological space.
Suppose that for any two different points ,
we can find two disjoint neighborhoods
such that their
closures are also disjoint:
Then we say that is a completely Hausdorff space or a space.
Notes
A synonym for functionally Hausdorff space is
Urysohn space [1].
Unfortunately, the definition of completely Hausdorff and
are not as standard as one would like since. For example, the
term completely Hausdorff space is also used to mean
a functionally Hausdorff space (e.g. [2]).
Nevertheless, in the present convention, we have the implication
:
which suggests why the name have been used to denote both completely Hausdorff spaces and functionally Hausdorff spaces.
References
- 1 L.A. Steen, J.A.Seebach, Jr., Counterexamples in topology, Holt, Rinehart and Winston, Inc., 1970.
- 2 S. Willard, General Topology, Addison-Wesley Publishing Company, 1970.
Title | completely Hausdorff |
---|---|
Canonical name | CompletelyHausdorff |
Date of creation | 2013-03-22 14:16:03 |
Last modified on | 2013-03-22 14:16:03 |
Owner | PrimeFan (13766) |
Last modified by | PrimeFan (13766) |
Numerical id | 15 |
Author | PrimeFan (13766) |
Entry type | Definition |
Classification | msc 54D10 |
Synonym | completely Hausdorff space |
Synonym | |
Synonym | Urysohn space |
Related topic | HausdorffSpaceNotCompletelyHausdorff |