Normal 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

In the T family (properties of topological spaces related to separation axioms), this is called: T4

Definition

Symbol-free definition

A topological space is said to be normal if all points in it are closed sets, and given any two disjoint closed sets in the topological space, there are disjoint open sets containing them.

Definition with symbols

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Relation with other properties

Stronger properties

• Compact Hausdorff space
• Hereditarily normal space
• Perfectly normal space
• Metrizable space
• CW-space

Weaker properties

• Completely regular space
• Regular space
• Hausdorff space
• T1 space
• Kolmogorov space