The Gelfand spectrum of a noncommutative C *-algebra : a topos-theoretic approach

@inproceedings{Heunen2010TheGS,
title={The Gelfand spectrum of a noncommutative C *-algebra : a topos-theoretic approach},
author={Chris Heunen and Nicolaas P. Landsman and Bas Spitters and Sander Wolters},
year={2010}
}

We compare two influential ways of defining a generalized notion of space. The first, inspired by Gelfand duality, states that the category of ‘noncommutative spaces’ is the opposite of the category of C*-algebras. The second, loosely generalizing Stone duality, maintains that the category of ‘point-free spaces’ is the opposite of the category of frames (that is, complete lattices in which the meet distributes over arbitrary joins). Earlier work by the first three authors shows how a… CONTINUE READING