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In mathematics and particularly in topology, pairwise Stone space is a bitopological space {\displaystyle \scriptstyle } 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 {\displaystyle \scriptstyle } is a spectral space, then {\displaystyle \scriptstyle } is a pairwise Stone space, where τ ∗ {\displaystyle \scriptstyle \tau ^{*}} is the de Groot dual topology of τ {\displaystyle \scriptstyle \tau } . Conversely, if {\displaystyle \scriptstyle } is a pairwise Stone space, then both {\displaystyle \scriptstyle } and {\displaystyle \scriptstyle } are spectral spaces.