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, Volume 30, Issue 2, pp 643–655 | Cite as

A Four for the Price of One Duality Principle for Distributive Spaces

  • Dirk Hofmann
Article

Abstract

In this paper we consider topological spaces as generalised orders and characterise those spaces which satisfy a (suitably defined) topological distributive law. Furthermore, we show that the category of these spaces is dually equivalent to a certain category of frames by simply observing that both sides represent the idempotents split completion of the same category.

Keywords

Topological space Ordered set Distributivity Disconnected space Idempotents split completion Duality 

Mathematics Subject Classifications (2010)

06A06 06A75 06D10 06D22 06D50 06D75 18C15 54A20 54F65 

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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Center for Research and Development in Mathematics and ApplicationsDepartment of Mathematics, University of AveiroAveiroPortugal

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