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• # Artykuł - szczegóły

## Bulletin of the Polish Academy of Sciences. Mathematics

2012 | 60 | 3 | 295-306

## Extending Maps in Hilbert Manifolds

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.

295-306

wydano
2012

### Twórcy

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