The space of ANR’s in ℝ n

Tadeusz Dobrowolski; Leonard Rubin

Fundamenta Mathematicae (1994)

  • Volume: 146, Issue: 1, page 31-58
  • ISSN: 0016-2736

Abstract

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The hyperspaces A N R ( ℝ n ) and A R ( ℝ n ) in 2 ℝ n ( n ≥ 3 ) consisting respectively of all compact absolute neighborhood retracts and all compact absolute retracts are studied. It is shown that both have the Borel type of absolute G δ σ δ -spaces and that, indeed, they are not F σ δ σ -spaces. The main result is that A N R ( ℝ n ) is an absorber for the class of all absolute G δ σ δ -spaces and is therefore homeomorphic to the standard model space Ω 3 of this class.

How to cite

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Dobrowolski, Tadeusz, and Rubin, Leonard. "The space of ANR’s in $ℝ^n$." Fundamenta Mathematicae 146.1 (1994): 31-58. <http://eudml.org/doc/212050>.

@article{Dobrowolski1994,
abstract = {The hyperspaces $ANR(ℝ^n)$ and $AR(ℝ^n)$ in $2^\{ℝ^n\} (n ≥ 3)$ consisting respectively of all compact absolute neighborhood retracts and all compact absolute retracts are studied. It is shown that both have the Borel type of absolute $G_\{δσ δ\}$-spaces and that, indeed, they are not $F_\{σ δσ \}$-spaces. The main result is that $ANR(ℝ^n)$ is an absorber for the class of all absolute $G_\{δσ δ\}$-spaces and is therefore homeomorphic to the standard model space $Ω_3$ of this class.},
author = {Dobrowolski, Tadeusz, Rubin, Leonard},
journal = {Fundamenta Mathematicae},
keywords = {hyperspace; absolute neighborhood retract; absolute retract; $G_\{δσ δ\}$-set; absorber; absorbing set},
language = {eng},
number = {1},
pages = {31-58},
title = {The space of ANR’s in $ℝ^n$},
url = {http://eudml.org/doc/212050},
volume = {146},
year = {1994},
}

TY - JOUR
AU - Dobrowolski, Tadeusz
AU - Rubin, Leonard
TI - The space of ANR’s in $ℝ^n$
JO - Fundamenta Mathematicae
PY - 1994
VL - 146
IS - 1
SP - 31
EP - 58
AB - The hyperspaces $ANR(ℝ^n)$ and $AR(ℝ^n)$ in $2^{ℝ^n} (n ≥ 3)$ consisting respectively of all compact absolute neighborhood retracts and all compact absolute retracts are studied. It is shown that both have the Borel type of absolute $G_{δσ δ}$-spaces and that, indeed, they are not $F_{σ δσ }$-spaces. The main result is that $ANR(ℝ^n)$ is an absorber for the class of all absolute $G_{δσ δ}$-spaces and is therefore homeomorphic to the standard model space $Ω_3$ of this class.
LA - eng
KW - hyperspace; absolute neighborhood retract; absolute retract; $G_{δσ δ}$-set; absorber; absorbing set
UR - http://eudml.org/doc/212050
ER -

References

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