The Sorgenfrey plane and the Niemytzki plane are Baire spaces

For the Moore plane: If a space has an dense subspace which is a Baire space, then the space itself is Baire. The open half-plane is dense in the Moore plane and is Baire.


Both your spaces are examples of pseudocomplete spaces (see my answer here for more links etc.) and are Baire for that reason.

Tags:

General Topology

Baire Category

Sorgenfrey Line

Moore Plane

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