The Convenient Setting of Global Analysis

  title={The Convenient Setting of Global Analysis},
  author={Andreas Kriegl and Peter W. Michor},
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. 
Holomorphic manifolds on locally convex spaces
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
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
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
. 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
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
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
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
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
. 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
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∞


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
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
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
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
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
Spaces of multilinear mappings.- Continuously differentiable functions.- Functions of class Cp.
Geometry of Banach Spaces: Selected Topics
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
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
  • S. Yamamuro
  • Mathematics
    Bulletin 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.