Moore space: Difference between revisions
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* [[Collectionwise normal and Moore implies metrizable]] | |||
* [[Traylor's theorem]]: Every [[metacompact space|metacompact]] [[separable space|separable]] [[normal space|normal]] Moore space is metrizable. | * [[Traylor's theorem]]: Every [[metacompact space|metacompact]] [[separable space|separable]] [[normal space|normal]] Moore space is metrizable. | ||
* [[Reed-Zenor theorem]]: Every [[locally compact space|locally compact]] [[locally connected space|locally connected]] [[normal space|normal]] Moore space is metrizable. | * [[Reed-Zenor theorem]]: Every [[locally compact space|locally compact]] [[locally connected space|locally connected]] [[normal space|normal]] Moore space is metrizable. | ||
* [[Jones' theorem]]: If <math>2^{\aleph_0} < 2^{\aleph_1}</math> then every [[separable space|separable]] [[normal space|normal]] Moore space is metrizable (i.e., we can drop the metacompactness assumption from Traylor's theorem). | * [[Jones' theorem]]: If <math>2^{\aleph_0} < 2^{\aleph_1}</math> then every [[separable space|separable]] [[normal space|normal]] Moore space is metrizable (i.e., we can drop the metacompactness assumption from Traylor's theorem). | ||
Latest revision as of 02:43, 27 January 2012
You might be looking for: Moore space of a group
This article defines a property of topological spaces: a property that can be evaluated to true/false for any topological space|View a complete list of properties of topological spaces
Definition
A topological space is termed a Moore space if it is regular and developable.
Relation with other properties
Stronger properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| metrizable space | metrizable implies Moore | |FULL LIST, MORE INFO |
Weaker properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| developable space | ||||
| regular space | ||||
| Hausdorff space |
Facts
- Collectionwise normal and Moore implies metrizable
- Traylor's theorem: Every metacompact separable normal Moore space is metrizable.
- Reed-Zenor theorem: Every locally compact locally connected normal Moore space is metrizable.
- Jones' theorem: If then every separable normal Moore space is metrizable (i.e., we can drop the metacompactness assumption from Traylor's theorem).