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Pairwise Stone space

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In mathematics and particularly in topology, pairwise Stone space is a bitopological space 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:[1] If is a spectral space, then is a pairwise Stone space, where is the de Groot dual topology of . Conversely, if is a pairwise Stone space, then both and are spectral spaces.

See also

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Notes

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  1. ^ G. Bezhanishvili, N. Bezhanishvili, D. Gabelaia, A. Kurz, (2010). Bitopological duality for distributive lattices and Heyting algebras. Mathematical Structures in Computer Science, 20.