Regular opens in constructive topology and a representation theorem for overlap algebras

Annals of Pure and Applied Logic 164 (4):421-436 (2013)
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Abstract

Giovanni Sambin has recently introduced the notion of an overlap algebra in order to give a constructive counterpart to a complete Boolean algebra. We propose a new notion of regular open subset within the framework of intuitionistic, predicative topology and we use it to give a representation theorem for overlap algebras. In particular we show that there exists a duality between the category of set-based overlap algebras and a particular category of topologies in which all open subsets are regular

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Citations of this work

Constructive version of Boolean algebra.F. Ciraulo, M. E. Maietti & P. Toto - 2013 - Logic Journal of the IGPL 21 (1):44-62.
Intuitionistic Overlap Structures.Francesco Ciraulo - 2013 - Logic and Logical Philosophy 22 (2):201-212.

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Compactness in locales and in formal topology.Steven Vickers - 2006 - Annals of Pure and Applied Logic 137 (1-3):413-438.

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