Protometrizable space
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
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Relation with other properties
Stronger properties
| property | quick description | proof of implication | proof of strictness (reverse implication failure) | intermediate notions |
|---|---|---|---|---|
| Metrizable space | underlying topology of a metric space | metrizable implies protometrizable | protometrizable not implies metrizable | |FULL LIST, MORE INFO |
| Manifold | ||||
| Closed sub-Euclidean space |
Weaker properties
| property | quick description | proof of implication | proof of strictness (reverse implication failure) | intermediate notions |
|---|---|---|---|---|
| Elastic space | ||||
| Monotonically normal space | |FULL LIST, MORE INFO | |||
| Hereditarily normal space | |FULL LIST, MORE INFO | |||
| Normal space | |FULL LIST, MORE INFO | |||
| Collectionwise normal space | |FULL LIST, MORE INFO | |||
| Hereditarily collectionwise normal space | |FULL LIST, MORE INFO |