Irreducible equivalence relations, Gleason spaces, and de Vries duality

Open Access
Authors
Publication date 06-2017
Journal Applied Categorical Structures
Volume | Issue number 25 | 3
Pages (from-to) 381-401
Organisations
  • Interfacultary Research - Institute for Logic, Language and Computation (ILLC)
Abstract By de Vries duality, the category of compact Hausdorff spaces is dually equivalent to the category of de Vries algebras (complete Boolean algebras endowed with a proximity-like relation). We provide an alternative “modal-like” duality by introducing the concept of a Gleason space, which is a pair (X,R), where X is an extremally disconnected compact Hausdorff space and R is an irreducible equivalence relation on X. Our main result states that the category of Gleason spaces is equivalent to the category of compact Hausdorff spaces, and is dually equivalent to the category of de Vries algebras.
Document type Article
Language English
Published at https://doi.org/10.1007/s10485-016-9434-2
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