Displaying similar documents to “Functor of extension in Hilbert cube and Hilbert space”

On extension of functors

L. Karchevska, Taras Radul (2012)

Commentationes Mathematicae Universitatis Carolinae

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A. Chigogidze defined for each normal functor on the category Comp an extension which is a normal functor on the category Tych. We consider this extension for any functor on the category Comp and investigate which properties it preserves from the definition of normal functor. We investigate as well some topological properties of such extension.

Spaces of measurable functions

Piotr Niemiec (2013)

Open Mathematics

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For a metrizable space X and a finite measure space (Ω, 𝔐 , µ), the space M µ(X) of all equivalence classes (under the relation of equality almost everywhere mod µ) of 𝔐 -measurable functions from Ω to X, whose images are separable, equipped with the topology of convergence in measure, and some of its subspaces are studied. In particular, it is shown that M µ(X) is homeomorphic to a Hilbert space provided µ is (nonzero) nonatomic and X is completely metrizable and has more than one point. ...

Topological groups and convex sets homeomorphic to non-separable Hilbert spaces

Taras Banakh, Igor Zarichnyy (2008)

Open Mathematics

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Let X be a topological group or a convex set in a linear metric space. We prove that X is homeomorphic to (a manifold modeled on) an infinite-dimensional Hilbert space if and only if X is a completely metrizable absolute (neighborhood) retract with ω-LFAP, the countable locally finite approximation property. The latter means that for any open cover 𝒰 of X there is a sequence of maps (f n: X → X)nεgw such that each f n is 𝒰 -near to the identity map of X and the family f n(X)n∈ω is locally...