Preregular space
Definition
A topological space is termed preregular if it satisfies the following equivalent conditions:
- Any two topologically distinguishable points can be separated by pairwise disjoint open subsets.
- Its Kolmogorov quotient is a Hausdorff 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
Relation with other properties
Stronger properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| Hausdorff space | |FULL LIST, MORE INFO | |||
| regular space | |FULL LIST, MORE INFO |
Weaker properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| symmetric space | Kolmogorov quotient is a T1 space. | |FULL LIST, MORE INFO |