Functions of class Ck without derivatives.

Tuynman, Gijs M.. "Functions of class Ck without derivatives.." Publicacions Matemàtiques 41.2 (1997): 417-435. <http://eudml.org/doc/41315>.

@article{Tuynman1997,
abstract = {We describe a general axiomatic way to define functions of class Ck, k ∈ N∪\{∞\} on topological abelian groups. In the category of Banach spaces, this definition coincides with the usual one. The advantage of this axiomatic approach is that one can dispense with the notion of norms and limit procedures. The disadvantage is that one looses the derivative, which is replaced by a local linearizing factor. As an application we use this approach to define C∞ functions in the setting of graded/super manifolds.},
author = {Tuynman, Gijs M.},
journal = {Publicacions Matemàtiques},
keywords = {Variedad graduada; Funciones de variable compleja; Geometría diferencial; Grupos abelianos; topological abelian groups; linearizing factor; functions of class },
language = {eng},
number = {2},
pages = {417-435},
title = {Functions of class Ck without derivatives.},
url = {http://eudml.org/doc/41315},
volume = {41},
year = {1997},
}

TY - JOUR
AU - Tuynman, Gijs M.
TI - Functions of class Ck without derivatives.
JO - Publicacions Matemàtiques
PY - 1997
VL - 41
IS - 2
SP - 417
EP - 435
AB - We describe a general axiomatic way to define functions of class Ck, k ∈ N∪{∞} on topological abelian groups. In the category of Banach spaces, this definition coincides with the usual one. The advantage of this axiomatic approach is that one can dispense with the notion of norms and limit procedures. The disadvantage is that one looses the derivative, which is replaced by a local linearizing factor. As an application we use this approach to define C∞ functions in the setting of graded/super manifolds.
LA - eng
KW - Variedad graduada; Funciones de variable compleja; Geometría diferencial; Grupos abelianos; topological abelian groups; linearizing factor; functions of class
UR - http://eudml.org/doc/41315
ER -