# Hereditarily normal Hausdorff space

From Topospaces

## Definition

A topological space is termed a **hereditarily normal Hausdorff space** if it satisfies the following equivalent conditions:

- It is both a hereditarily normal space and a Hausdorff space.
- It is both a hereditarily normal space and a T1 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:* T5