Let be the category of locally compact Hausdorff spaces with continuous proper maps as morphisms. And, let be the category of commutative -algebras with proper *-homomorphisms (send approximate units into approximate units) as morphisms. There is a contravariant functor which sends each locally compact Hausdorff space to the commutative -algebra ( if is compact). Conversely, there is a contravariant functor which sends each commutative -algebra to the space of characters on (with the Gelfand topology).
|Date of creation||2013-03-22 13:29:28|
|Last modified on||2013-03-22 13:29:28|
|Last modified by||mhale (572)|