High Quality Content by WIKIPEDIA articles! In mathematics and particularly in topology, pairwise Stone space is a bitopological space scriptstyle (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 scriptstyle (X,tau) is a spectral space, then scriptstyle (X,tau,tau^*) is a pairwise Stone space, where scriptstyle tau^* is the de Groot dual topology of scriptstyle tau . Conversely, if scriptstyle (X,tau_1,tau_2) is a pairwise Stone space, then both scriptstyle (X,tau_1) and scriptstyle (X,tau_2) are spectral spaces.

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