# Product-transitively paracompact 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 compactness. View other variations of compactness

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

## Contents

## Definition

### Symbol-free definition

A topological space is termed **product-transitively paracompact** if its product with any paracompact space is paracompact.

## Formalisms

### In terms of the product-transiter operator

*This property is obtained by applying the product-transiter operator to the property: paracompactness*

## Relation with other properties

### Stronger properties

### Weaker properties

## Metaproperties

### Products

*This property of topological spaces is closed under taking finite products*

Any finite product of product-transitively paracompact spaces is again product-transitively paracompact. This follows from the general theory of product-transiters.