Editing Exterior algebra (section)

=== Superspace ===
The exterior algebra over the complex numbers is the archetypal example of a [[superalgebra]], which plays a fundamental role in physical theories pertaining to [[fermion]]s and [[supersymmetry]].  A single element of the exterior algebra is called a '''supernumber'''<ref>{{cite book |author-link=Bryce DeWitt |first=Bryce |last=DeWitt  |title=Supermanifolds |year=1984 |publisher=Cambridge University Press  |isbn=0-521-42377-5 |chapter=Chapter 1 |page=1}}</ref> or [[Grassmann number]].  The exterior algebra itself is then just a one-dimensional [[superspace]]: it is just the set of all of the points in the exterior algebra.  The topology on this space is essentially the [[weak topology]], the [[open sets]] being the [[cylinder set]]s.  An {{math|''n''}}-dimensional superspace is just the {{tmath|n}}-fold product of exterior algebras.