completely Hausdorff
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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.
Synonym:
completely Hausdorff space, $T_{2\frac{1}{2}}$,Urysohn space
Type of Math Object:
Definition
Major Section:
Reference
Groups audience:
Mathematics Subject Classification
54D10 no label found
