Half-side formula

In mathematics and particularly in topology, pairwise Stone space is a bitopological space $(X,{\tau }_1,{\tau }_2)$ which is pairwise compact, pairwise Hausdorff, and pairwise zero-dimensional.

Pairwise Stone spaces are a bitopological version of the Stone spaces.

Pairwise Stone spaces are closely related to spectral spaces.

Theorem: If $(X,\tau )$ is a spectral space, then $(X,\tau ,{\tau }^{*})$ is a pairwise Stone space, where ${\tau }^{*}$ is the de Groot dual topology of $\tau$ . Conversely, if $(X,{\tau }_1,{\tau }_2)$ is a pairwise Stone space, then both $(X,{\tau }_1)$ and $(X,{\tau }_2)$ are spectral spaces.

See also

• Bitopological space
• Duality theory for distributive lattices

Notes

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.