P-space

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

Definition

A topological space is termed a P-space if every $G_{\delta }$-subset in it is open.

Formalisms

Subspace property implication formalism

This property of topological spaces can be encoded by the fact that one subspace property implies another

The property of being a P-space can be described as the following implication between properties of subsets:

$G_{\delta }\implies$ Open

Relation with other properties

Stronger properties

• Alexandroff space

Weaker properties

• P'-space
• Countably orthocompact space