# Monotonically 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

*This article or section of article is sourced from*:Wikipedia

## Contents

## Definition

### Definition with symbols

A topological space is termed **monotonically normal** if there exists an operator from ordered pairs of disjoint closed sets to open sets, such that:

- For any disjoint closed subsets , contains and its closure is disjoint from
- If and with all four sets being closed, and disjoint from , we have:

This is the *monotonicity* condition. Such an operator is termed a monotone normality operator.

## Relation with other properties

### Stronger properties

### Weaker properties

### Incomparable 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

Any subspace of a monotonically normal space is monotonically normal.