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Embedded surfaces in the 3-torus

Allan L. Edmonds (2008)

Fundamenta Mathematicae

Those maps of a closed surface to the three-dimensional torus that are homotopic to embeddings are characterized. Particular attention is paid to the more involved case when the surface is nonorientable.

Embedding solenoids

Alex Clark, Robbert Fokkink (2004)

Fundamenta Mathematicae

A generalized solenoid is an inverse limit space with bonding maps that are (regular) covering maps of closed compact manifolds. We study the embedding properties of solenoids in linear space and in foliations.

Extending Maps in Hilbert Manifolds

Piotr Niemiec (2012)

Bulletin of the Polish Academy of Sciences. Mathematics

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 ) f ( A ) ¯ = , then for every open cover of M there is a map g:...

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