Stable maps into the Hilbert cube

Garity, Dennis J.; Rohm, Dale M.

doi:10.1090/s0002-9939-1988-0962840-4

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2008

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“…Here, π n : I ∞ → I n is the projection onto I n and S n−1 is the boundary of I n . On the other hand, a map f : X → I ∞ is essential if and only if f is universal (this fact was established in [12] for metrizable compact spaces, but the proof works for arbitrary compact spaces). Theorem 3.6.…”

Section: Now Definementioning

confidence: 99%

Generalized Cantor manifolds and homogeneity

Karassev,

Krupski,

Todorov

et al. 2008

Preprint

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A classical theorem of Alexandroff states that every n-dimensional compactum X contains an n-dimensional Cantor manifold. This theorem has a number of generalizations obtained by various authors. We consider extension-dimensional and infinite dimensional analogs of strong Cantor manifolds, Mazurkiewicz manifolds, and V n -continua, and prove corresponding versions of the above theorem. We apply our results to show that each homogeneous metrizable continuum which is not in a given class C is a strong Cantor manifold (or at least a Cantor manifold) with respect to C. Here, the class C is one of four classes that are defined in terms of dimension-like invariants. A class of spaces having bases of neighborhoods satisfying certain special conditions is also considered.

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Section: Now Definementioning

confidence: 99%