Geodesic
The space of ANR’s in $ℝ^n$
Fundamenta Mathematicae, Tome 146 (1994) no. 1, pp. 31-58

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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.
DOI : 10.4064/fm-146-1-31-58
Keywords: hyperspace, absolute neighborhood retract, absolute retract, $G_{δσ δ}$-set, absorber

Tadeusz Dobrowolski 1 ; Leonard R. Rubin 1

1 
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Tadeusz Dobrowolski; Leonard R. Rubin. The space of ANR’s in $ℝ^n$. Fundamenta Mathematicae, Tome 146 (1994) no. 1, pp. 31-58. doi: 10.4064/fm-146-1-31-58

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