Localic Metric spaces and the localic Gelfand duality

Simon Henry

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arXiv · 1411.0898

Localic Metric spaces and the localic Gelfand duality

Simon Henry

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Abstract

In this paper we prove, as conjectured by B.Banachewski and C.J.Mulvey, that the constructive Gelfand duality can be extended into a duality between compact regular locales and unital abelian localic C*-algebras. In order to do so we develop a constructive theory of localic metric spaces and localic Banach spaces, we study the notion of localic completion of such objects and the behaviour of these constructions with respect to pull-back along geometric morphisms.

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Simon Henry. 2014-11-04. Localic Metric spaces and the localic Gelfand duality. https://arxiv.org/abs/1411.0898

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