nLab P-space

Definition

A P-space is a topological space in which every $G_\delta$ subset is open or equivalently every $F_\sigma$ 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).

Related concepts

• G-delta subspace

References

See also

• Wikipedia P-space