In mathematics

Mathematics

Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

 and particularly in topology

Topology

Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...

, pairwise Stone space is a bitopological space

Bitopological space

In mathematics, a bitopological space is a set endowed with two topologies. Typically, if the set is X and the topologies are \sigma and \tau then we refer to the bitopological space as .-Bi-continuity:...

  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 space

Spectral space

In mathematics, a spectral space is a topological space which is homeomorphic to the spectrum of a commutative ring.-Definition:Let X be a topological space and let K\circ be the set of allquasi-compact and open subsets of X...

s.

Theorem: If is a spectral space, then is a pairwise Stone space, where is the de Groot dual

De Groot dual

In mathematics, in particular in topology, the de Groot dual of a topology τ on a set X is the topology τ* whose closed sets are generated by compact saturated subsets of .- References :...

topology of . Conversely, if is a pairwise Stone space, then both and are spectral spaces.