Certain results on extending maps taking values in Hilbert manifolds by maps which are close to being embeddings are presented. Sufficient conditions on a map under which it is extendable by an embedding are given. In particular, it is shown that if X is a completely metrizable space of topological weight not greater than α ≥ ℵ₀, A is a closed set in X and f: X → M is a map into a manifold M modelled on a Hilbert space of dimension α such that , then for every open cover of M there is a map g: X → M which is -close to f (on X), coincides with f on A and is an embedding of X∖A into M. If, in addition, X∖A is a connected manifold modelled on the same Hilbert space as M, and is a Z-set in M, then the above map g may be chosen so that be an open embedding.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba60-3-9,
author = {Piotr Niemiec},
title = {Extending Maps in Hilbert Manifolds},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {60},
year = {2012},
pages = {295-306},
zbl = {1253.57012},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba60-3-9}
}
Piotr Niemiec. Extending Maps in Hilbert Manifolds. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 60 (2012) pp. 295-306. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba60-3-9/