nLab P-space

Redirected from "P-spaces".
Contents

Context

Topology

topology (point-set topology, point-free topology)

see also differential topology, algebraic topology, functional analysis and topological homotopy theory

Introduction

Basic concepts

Universal constructions

Extra stuff, structure, properties

Examples

Basic statements

Theorems

Analysis Theorems

topological homotopy theory

Contents

Definition

A P-space is a topological space in which every G δG_\delta subset is open or equivalently every F σF_\sigma subset is closed.

Properties

Lemma

Alexandroff spaces are P-spaces.

This follows since even arbitary intersections of open sets are per definition open in Alexandroff spaces.
Lemma

P-spaces are countably orthocompact.

This follows since every countable open covering of a P-space is inner-preserving (meaning that for every point the intersection of all open sets of the open covering containing it is open).

References

See also

Created on March 20, 2024 at 14:18:45. See the history of this page for a list of all contributions to it.