In mathematics and particularly in topology, pairwise Stone space is a bitopological space
(
X
,
τ
1
,
τ
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
,
τ
)
is a spectral space, then
(
X
,
τ
,
τ
∗
)
is a pairwise Stone space, where
τ
∗
is the de Groot dual topology of
τ
. Conversely, if
(
X
,
τ
1
,
τ
2
)
is a pairwise Stone space, then both
(
X
,
τ
1
)
and
(
X
,
τ
2
)
are spectral spaces.
