• Corpus ID: 14230542

# REMARKS ON GERMS IN INFINITE DIMENSIONS

@inproceedings{Kriegl1997REMARKSOG,
title={REMARKS ON GERMS IN INFINITE DIMENSIONS},
author={Andreas Kriegl},
year={1997}
}
Smooth, real analytic and holomorphic mappings defined on non-open subsets of infinite dimensional vector spaces are treated.
The Convenient Setting of Global Analysis
• Mathematics
• 1997
Introduction Calculus of smooth mappings Calculus of holomorphic and real analytic mappings Partitions of unity Smoothly realcompact spaces Extensions and liftings of mappings Infinite dimensional
A Survey on Frölicher Spaces
Abstract This survey paper highlights a series of results in recent research on topology, geometry and categorical properties of spaces provided with a new structure in the mathematical literature,
H\"older--Zygmund classes on smooth curves
. We prove that a function in several variables is in the local Zyg- mund class Z m, 1 if and only if its composite with every smooth curve is of class Z m, 1 . This complements the well-known
Extending Whitney’s extension theorem: nonlinear function spaces
• Mathematics
Annales de l'Institut Fourier
• 2021
This article shows that there is a continuous extension operator for compactly-supported smooth sections of vector bundles on possibly non-compact smooth manifolds, where the closed set to which
Diffeological, Frölicher, and Differential Spaces
• Mathematics
• 2017
Differential calculus on Euclidean spaces has many generalisations. In particular, on a set $X$, a diffeological structure is given by maps from open subsets of Euclidean spaces to $X$, a
Arc-smooth functions and cuspidality of sets
. A function f is arc-smooth if the composite f ◦ c with every smooth curve c in its domain of deﬁnition is smooth. On open sets in smooth manifolds the arc-smooth functions are precisely the smooth
O-Minimality and its Applications to Number Theory and Analysis
• Mathematics
• 2018
The workshop brought together researchers in the areas of ominimal structures, analysis and number theory. The latest developments in o-minimality and their applications to number theory and analysis
Arc-smooth functions on closed sets
• A. Rainer
• Mathematics
Compositio Mathematica
• 2019
By an influential theorem of Boman, a function $f$ on an open set $U$ in $\mathbb{R}^{d}$ is smooth ( ${\mathcal{C}}^{\infty }$ ) if and only if it is arc-smooth, that is, $f\,\circ \,c$ is smooth
Convenient Categories of Smooth Spaces
• Mathematics
• 2008
A "Chen space" is a set X equipped with a collection of "plots" - maps from convex sets to X - satisfying three simple axioms. While an individual Chen space can be much worse than a smooth manifold,

## References

SHOWING 1-10 OF 13 REFERENCES
Linear Spaces And Differentiation Theory
• Mathematics
• 1988
Preface Foundational Material Convenient Vector Spaces Multilinear Maps and Categorical Properties Calculus in Convenient Vector Spaces Differentiable Maps and Categorical Properties The Mackey
The convenient setting for real analytic mappings
• Mathematics
• 1990
We present here "the" cartesian closed theory for real analytic mappings. It is based on the concept of real analytic curves in locally convex vector spaces. A mapping is real analytic, if it maps
Die richtigen Räume für Analysis im Unendlich-Dimensionalen
The aim of this paper is to characterize those locally convex spaces, which have the following properties. 1. Any curve, which is differentiable if composed with continuous linear forms, is
A convenient setting for holomorphy
• Mathematics
• 1985
© Andrée C. Ehresmann et les auteurs, 1985, tous droits réservés. L’accès aux archives de la revue « Cahiers de topologie et géométrie différentielle catégoriques » implique l’accord avec les
"J."
however (for it was the literal soul of the life of the Redeemer, John xv. io), is the peculiar token of fellowship with the Redeemer. That love to God (what is meant here is not God’s love to men)
Teubner
• Stuttgart,
• 1981
Extensions of C 1 -functions deened in a half space
• Proc. AMS
• 1964
Institut f ur Mathematik der Universitt at Wien, Strudlhofgasse4, A-1090 Wien, Austria, e-mail: Andreas.Kriegl@univie.ac
• Institut f ur Mathematik der Universitt at Wien, Strudlhofgasse4, A-1090 Wien, Austria, e-mail: Andreas.Kriegl@univie.ac
Analytic extensions of diierentiable functions deened in closed sets
• 63{89. W43] , Diierentiable Even Functions
• 1934