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Mappings on the dyadic solenoid

Jan M. Aarts, Robbert J. Fokkink (2003)

Commentationes Mathematicae Universitatis Carolinae

Answering an open problem in [3] we show that for an even number k , there exist no k to 1 mappings on the dyadic solenoid.

Maps with dimensionally restricted fibers

Vesko Valov (2011)

Colloquium Mathematicae

We prove that if f: X → Y is a closed surjective map between metric spaces such that every fiber f - 1 ( y ) belongs to a class S of spaces, then there exists an F σ -set A ⊂ X such that A ∈ S and d i m f - 1 ( y ) A = 0 for all y ∈ Y. Here, S can be one of the following classes: (i) M: e-dim M ≤ K for some CW-complex K; (ii) C-spaces; (iii) weakly infinite-dimensional spaces. We also establish that if S = M: dim M ≤ n, then dim f ∆ g ≤ 0 for almost all g C ( X , n + 1 ) .

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