# 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

### Symbol-free definition

A topological space is termed **collectionwise normal** if it is T1 and, given any *discrete* collection of closed sets (viz., a disjoint collection of closed sets such that the union of any subcollection is closed), there exists a family of pairwise disjoint open sets containing each of the closed sets.

## Relation with other properties

### Stronger properties

- Metrizable space
- Elastic space
- Linearly orderable space
- Monotonically normal space
- Hereditarily collectionwise normal space