Moore space
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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).
