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Homotopical dynamics.

Marzantowicz, Wacław (2003)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

Hopfian and strongly hopfian manifolds

Young Im, Yongkuk Kim (1999)

Fundamenta Mathematicae

Let p: M → B be a proper surjective map defined on an (n+2)-manifold such that each point-preimage is a copy of a hopfian n-manifold. Then we show that p is an approximate fibration over some dense open subset O of the mod 2 continuity set C’ and C’ ∖ O is locally finite. As an application, we show that a hopfian n-manifold N is a codimension-2 fibrator if χ(N) ≠ 0 or H 1 ( N ) 2

Hyperspaces of Finite Sets in Universal Spaces for Absolute Borel Classes

Kotaro Mine, Katsuro Sakai, Masato Yaguchi (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

By Fin(X) (resp. F i n k ( X ) ), we denote the hyperspace of all non-empty finite subsets of X (resp. consisting of at most k points) with the Vietoris topology. Let ℓ₂(τ) be the Hilbert space with weight τ and f ( τ ) the linear span of the canonical orthonormal basis of ℓ₂(τ). It is shown that if E = f ( τ ) or E is an absorbing set in ℓ₂(τ) for one of the absolute Borel classes α ( τ ) and α ( τ ) of weight ≤ τ (α > 0) then Fin(E) and each F i n k ( E ) are homeomorphic to E. More generally, if X is a connected E-manifold then Fin(X) is homeomorphic...

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