Preregular space

From Topospaces
Jump to: navigation, search

Definition

A topological space is termed preregular if it satisfies the following equivalent conditions:

  1. Any two topologically distinguishable points can be separated by pairwise disjoint open subsets.
  2. 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