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Functor of extension in Hilbert cube and Hilbert space

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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.

Ograniczanie wyników

1 Open Mathematics

1 Niemiec P.

1 2014

Wyniki wyszukiwania

Functor of extension in Hilbert cube and Hilbert space