Extending Maps in Hilbert Manifolds

• Autorzy: Piotr Niemiec
• Języki publikacji: EN

Abstrakty

EN

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 $f(X∖A) ∩ \overline{f(∂A)} = ∅$, then for every open cover 𝒰 of M there is a map g: X → M which is 𝒰-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 $\overline{f(∂A)}$ is a Z-set in M, then the above map g may be chosen so that $g|_{X∖A}$ be an open embedding.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2012
• Tom: 60
• Numer: 3
• Strony: 295-306

Daty

wydano

2012

Twórcy

autor

Piotr Niemiec

• Instytut Matematyki, Wydział Matematyki i Informatyki, Uniwersytet Jagielloński, Łojasiewicza 6, 30-348 Kraków, Poland

Identyfikatory

DOI

10.4064/ba60-3-9