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Functor of extension in Hilbert cube and Hilbert space

100%

Niemiec P.

Open Mathematics

2014

tom 12

nr 6

887-895

It is shown that if Ω = Q or Ω = ℓ 2, then there exists a functor of extension of maps between Z-sets in Ω to mappings of Ω into itself. This functor transforms homeomorphisms into homeomorphisms, thus giving a functorial setting to a well-known theorem of Anderson [Anderson R.D., On topological infinite deficiency, Michigan Math. J., 1967, 14, 365–383]. It also preserves convergence of sequences of mappings, both pointwise and uniform on compact sets, and supremum distances as well as uniform continuity, Lipschitz property, nonexpansiveness of maps in appropriate metrics.

Spaces of measurable functions

88%

Niemiec P.

Open Mathematics

2013

tom 11

nr 7

1304-1316

For a metrizable space X and a finite measure space (Ω, $\mathfrak{M}$, µ), the space M µ(X) of all equivalence classes (under the relation of equality almost everywhere mod µ) of $\mathfrak{M}$-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.

Ograniczanie wyników

2 Open Mathematics

2 Niemiec P.

1 2014

1 2013

Wyniki wyszukiwania

Functor of extension in Hilbert cube and Hilbert space

Spaces of measurable functions