# nLab constructive Gelfand duality theorem

### Context

#### Topos Theory

Could not include topos theory - contents

# Contents

## Idea

There is a statement and proof of Gelfand duality in constructive mathematics. This therefore makes sense in any topos.

## References

A proof of Gelfand duality claimed to be constructive was given in.

• Bernhard Banaschewski; Christopher J. Mulvey, A globalisation of the Gelfand duality theorem Annals of Pure and Applied Logic, 137(1–3):62–103, 2006

This uses however Barr's theorem which requires itself non-constructive logic and requires the ambient topos to be a Grothendieck topos

A fully constructive proof is claimed in

• Thierry Coquand, Bas Spitters, Constructive Gelfand duality for $C^*$-algebras , Mathematical Proceedings of the Cambridge Philosophical society , Volume 147, Issue 02, September 2009, pp 323-337 (arXiv:0808.1518)

A review of some aspects of constructive Gelfand duality is in section 2 of

Revised on April 9, 2014 05:45:42 by Tim Porter (2.26.27.237)