Hausdorff implies T1: Difference between revisions
(Created page with '{{topospace property implication| stronger = Hausdorff space| weaker = T1 space}} ==Statement== Any Hausdorff space is a T1 space. ==Related facts== * [[Hausdorff imp…') |
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stronger = Hausdorff space| | stronger = Hausdorff space| | ||
weaker = T1 space}} | weaker = T1 space}} | ||
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* [[US not implies Hausdorff]] | * [[US not implies Hausdorff]] | ||
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The proof is direct from the definitions. | The proof is direct from the definitions. | ||
Latest revision as of 04:36, 30 January 2014
This article gives the statement and possibly, proof, of an implication relation between two topological space properties. That is, it states that every topological space satisfying the first topological space property (i.e., Hausdorff space) must also satisfy the second topological space property (i.e., T1 space)
View all topological space property implications | View all topological space property non-implications
Get more facts about Hausdorff space|Get more facts about T1 space
Statement
Any Hausdorff space is a T1 space.
Related facts
- Hausdorff implies US
- Hausdorff implies KC
- Hausdorff implies sober
- T1 not implies Hausdorff
- KC not implies Hausdorff
- US not implies Hausdorff
Proof
The proof is direct from the definitions.