## 9 Citations

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

- Mathematics
- 2015

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

- Mathematics
- 2022

. 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

- MathematicsAnnales 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

- Mathematics
- 2021

. 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

- MathematicsCompositio 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

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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

- Mathematics
- 1982

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."

- PhilosophyThe New Yale Book of Quotations
- 2021

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