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.
@article{bwmeta1.element.doi-10_2478_s11533-013-0386-6,
author = {Piotr Niemiec},
title = {Functor of extension in Hilbert cube and Hilbert space},
journal = {Open Mathematics},
volume = {12},
year = {2014},
pages = {887-895},
zbl = {1307.54021},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0386-6}
}
Piotr Niemiec. Functor of extension in Hilbert cube and Hilbert space. Open Mathematics, Tome 12 (2014) pp. 887-895. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0386-6/
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