Product-transitively paracompact space

From Topospaces
Jump to: navigation, search
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

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.