# The Convenient Setting of Global Analysis

@inproceedings{Kriegl1997TheCS, title={The Convenient Setting of Global Analysis}, author={Andreas Kriegl and Peter W. Michor}, year={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 manifolds Calculus on infinite dimensional manifolds Infinite dimensional differential geometry Manifolds of mappings Further applications References Index.

## 1,152 Citations

Holomorphic manifolds on locally convex spaces

- Mathematics
- 2005

Based on locally compact perturbations of the identity map similar to the Fredholm structures on real Banach manifolds, complex manifolds with inverse mapping theorem as part of the defintion are…

Sheaves of nonlinear generalized function spaces

- Mathematics
- 2017

We provide a framework for the construction of diffeomorphism invariant sheaves of nonlinear generalized functions spaces. As an application, global algebras of generalized functions for…

Flux Homomorphisms and Principal Bundles over Infinite Dimensional Manifolds

- Mathematics
- 2002

Abstract. Flux homomorphisms for closed vector-valued differential forms on infinite dimensional manifolds are defined. We extend the relation between the kernel of the flux for a closed 2-form ω and…

Examples of differentiable mappings into non-locally convex spaces

- Mathematics
- 2003

. Examples of diﬀerentiable mappings into real or complex topological vector spaces with speciﬁc properties are given, which illustrate the diﬀerences between diﬀerential calculus in the locally…

Integrability on Direct Limit Banach manifolds

- Mathematics
- 2014

This paper is devoted to the framework of direct limit of anchored Banach bundles over a convenient manifold which is a direct limit of Banach manifold. In particular we give a criterion of…

An algebraic approach to manifold-valued generalized functions

- Mathematics
- 2012

We discuss the nature of structure-preserving maps of varies function algebras. In particular, we identify isomorphisms between special Colombeau algebras on manifolds with invertible manifold-valued…

ULTRAMETRIC AND NON-LOCALLY CONVEX ANALOGUES OF THE GENERAL CURVE LEMMA OF CONVENIENT DIFFERENTIAL CALCULUS

- MathematicsGlasgow Mathematical Journal
- 2008

Abstract The General Curve Lemma is a tool of Infinite-Dimensional Analysis that enables refined studies of differentiability properties of maps between real locally convex spaces to be made. In this…

Synthetic Geometry of Manifolds

- Mathematics
- 2009

Preface 1. Calculus and linear algebra 2. Geometry of the neighbour relation 3. Combinatorial differential forms 4. The tangent bundle 5. Groupoids 6. Lie theory non-abelian covariant derivative 7.…

Implicit Functions from Topological Vector Spaces to Banach Spaces

- Mathematics
- 2003

. We prove implicit function theorems for mappings on topological vector spaces over valued ﬁelds. In the real and complex cases, we obtain implicit function theorems for mappings from arbitrary (not…

Extension of smooth functions in infinite dimensions II: manifolds

- Mathematics
- 2002

Let M be a separable C∞ Finsler manifold of infinite dimension. Then it is proved, amongst other results, that under suitable conditions of local extensibility the germ of a C∞ function, or of a C∞…

## References

SHOWING 1-10 OF 679 REFERENCES

REMARKS ON GERMS IN INFINITE DIMENSIONS

- Mathematics
- 1997

Smooth, real analytic and holomorphic mappings defined on non-open subsets of infinite dimensional vector spaces are treated.

On the convenient setting for real analytic mappings

- Mathematics
- 1993

We give an explicit description of the “convenient structure” onCω(ℝ, ℝ) defined in [3] yielding a much easier proof of cartesian closedness of the category of real analytic mappings between…

Algebras of real analytic functions; Homomorphisms and bounding sets

- Mathematics
- 1993

In this paper weare interested in subsets of a real Banach space on which different classes of functions are bounded.

The manifold structure of maps between open manifolds

- Mathematics
- 1993

We establish in a canonical manner a manifold structure for the completed space of bounded maps between open manifoldsM andN, assuming thatM andN are endowed with Riemannian metrics of bounded…

Homomorphisms on some function algebras

- Mathematics
- 1991

In this note we prove, for some classes of real locally convex spacesE including all complete Schwartz spaces, that every non-zero homomorphism on the algebraC∞ (E) ofC∞-functions onE is given by a…

Differential Calculus in Locally Convex Spaces

- Mathematics
- 1974

Spaces of multilinear mappings.- Continuously differentiable functions.- Functions of class Cp.

Geometry of Banach Spaces: Selected Topics

- Mathematics
- 1975

Support functionals for closed bounded convex subsets of a Banach space.- Convexity and differentiability of norms.- Uniformly convex and uniformly smooth Banach spaces.- The classical renorming…

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…

Notes on the inverse mapping theorem in locally convex spaces

- MathematicsBulletin of the Australian Mathematical Society
- 1980

Several problems arising from a functional analytic study on Omori's inverse mapping theorem are considered arriving at an inverse mapping theorem in locally convex spaces.