A synonym for functionally Hausdorff space is Urysohn space . 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. ). 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.
- 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.
|Date of creation||2013-03-22 14:16:03|
|Last modified on||2013-03-22 14:16:03|
|Last modified by||PrimeFan (13766)|
|Synonym||completely Hausdorff space|