Calculus in Vector Spaces without Norm by A. Frölicher, W. BucherEnglish | PDF | 1966 | 159 Pages | ISBN : 3540036121 | 6.9 MB
As emphasized by J. calculus primarily deals with the approximation (in a neighborhood of some point) of given mappings of vector spaces by linear mappings. The approximating linear map has to be a "good" approximation in some precise sense: it has to be "tangent" to the given map. A very useful notion of "tangent" can easily be introduced for maps between normed vector spaces; it leads to the notion of mappings and gives, in particular for Banach spaces, a very satisfactory theory (cf. Chap. VIII of [3]).