General forms of inverse and implicit function theorems, treatment closer to intuition through nonstandard techniques
General forms of inverse and implicit function theorems, treatment closer to intuition through nonstandard techniques
J. Dieudonné and M. Behrens using the notion of uniform differentiability have generalized for the case of Banach space the local inverse and implicit function theorems, respectively. The authors have shown that for a nonstandard treatment the various neighborhoods of a point that come into consideration in these papers can be replaced by the monad of the point. This focusses and clears up certain subtleties such as the internality aspects.
Nonstandard functional analysis, Derivatives of functions in infinite-dimensional spaces, monad, nonstandard treatment, Nonstandard analysis, uniform differentiability, local inverse and implicit function theorems
Nonstandard functional analysis, Derivatives of functions in infinite-dimensional spaces, monad, nonstandard treatment, Nonstandard analysis, uniform differentiability, local inverse and implicit function theorems