Perfectly normal space

In the T family (properties of topological spaces related to separation axioms), this is called: T6

This is a variation of normality. View other variations of normality

Definition

A topological space is termed perfectly normal if it is normal and every closed subset is a G-delta subset ($G_{\delta }$).

Relation with other properties

Stronger properties

• Metrizable space
• CW-space

Weaker properties

• Hereditarily normal space
• Normal space
• Perfect space

Metaproperties

Hereditariness

This property of topological spaces is hereditary, or subspace-closed. In other words, any subspace (subset with the subspace topology) of a topological space with this property also has this property.
View other subspace-hereditary properties of topological spaces

Any subspace of a perfectly normal space is perfectly normal.