Christoffel revisited

Abstract

This thesis discusses E. B. Christoffel's famous article from 1869 (an English translation is also included), generalises it to the more general setting of locally convex Hausdorff topological vector spaces over R or C, and furthermore estab- lishes a partial converse to the results of Christoffel in Banach spaces. Apart from this we rigorously discuss the aforementioned more general setting by in- troducing the concepts related to this setting from the ground up. This includes in particular a non-standard notion for the derivative and proofs of many useful statements, among which the open mapping theorem, closed graph theorem, fundamental theorem of integration, and the Taylor approximation theorem.