# Hereditarily collectionwise normal space

From Topospaces

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

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

## Contents

## Definition

A topological space is termed **hereditarily collectionwise normal** or **completely collectionwise normal** if it satisfies the following two conditions:

- every subspace of it is collectionwise normal
- every almost discrete collection of closed subsets can be separated by pairwise disjoint open subsets (here,
*almost discrete*means discrete in the union).

## Formalisms

### In terms of the hereditarily operator

*This property is obtained by applying the hereditarily operator to the property: collectionwise normal space*

## Relation with other properties

### Stronger properties

### Weaker properties

## 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