# Functor of extension in Hilbert cube and Hilbert space

Open Mathematics (2014)

- Volume: 12, Issue: 6, page 887-895
- ISSN: 2391-5455

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topPiotr Niemiec. "Functor of extension in Hilbert cube and Hilbert space." Open Mathematics 12.6 (2014): 887-895. <http://eudml.org/doc/269407>.

@article{PiotrNiemiec2014,

abstract = {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.},

author = {Piotr Niemiec},

journal = {Open Mathematics},

keywords = {Z-set; Functor of extension; Hilbert cube; Fréchet space; -set; Functor},

language = {eng},

number = {6},

pages = {887-895},

title = {Functor of extension in Hilbert cube and Hilbert space},

url = {http://eudml.org/doc/269407},

volume = {12},

year = {2014},

}

TY - JOUR

AU - Piotr Niemiec

TI - Functor of extension in Hilbert cube and Hilbert space

JO - Open Mathematics

PY - 2014

VL - 12

IS - 6

SP - 887

EP - 895

AB - 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.

LA - eng

KW - Z-set; Functor of extension; Hilbert cube; Fréchet space; -set; Functor

UR - http://eudml.org/doc/269407

ER -

## References

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