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A correction of two papers concerning Hilbert manifolds

H. Toruńczyk (1985)

Fundamenta Mathematicae

A general approximation theorem for Hilbert cube manifolds

T. A. Chapman (1983)

Compositio Mathematica

A generalization of Steenrod’s approximation theorem

Christoph Wockel (2009)

Archivum Mathematicum

In this paper we aim for a generalization of the Steenrod Approximation Theorem from [16, Section 6.7], concerning a smoothing procedure for sections in smooth locally trivial bundles. The generalization is that we consider locally trivial smooth bundles with a possibly infinite-dimensional typical fibre. The main result states that a continuous section in a smooth locally trivial bundles can always be smoothed out in a very controlled way (in terms of the graph topology on spaces of continuous...

Absolute Z-sets

Jean Lenaburg (1974)

Fundamenta Mathematicae

An embedding theorem of infinite-dimensional manifold pairs in the model space

Katsuro Sakai (1978)

Fundamenta Mathematicae

Arithmetic groups of gauge transformations.

C.W. Stark (1993)

Forum mathematicum

Banachian Differentiable Spaces.

M. Breuer, Ch.D. Marshall (1978)

Mathematische Annalen

Canonical Lipschitz structures on compact Hilbert cube manifolds

Jouni Luukkainen (1985)

Commentationes Mathematicae Universitatis Carolinae

Caractérisation topologique de l'espace des fonctions dérivables

Robert Cauty (1991)

Fundamenta Mathematicae

Central extensions of infinite-dimensional Lie groups

Karl-Hermann Neeb (2002)

Annales de l’institut Fourier

The main result of the present paper is an exact sequence which describes the group of central extensions of a connected infinite-dimensional Lie group $G$ by an abelian group $Z$ whose identity component is a quotient of a vector space by a discrete subgroup. A major point of this result is that it is not restricted to smoothly paracompact groups and hence applies in particular to all Banach- and Fréchet-Lie groups. The exact sequence encodes in particular precise obstructions for a given Lie algebra...