The space of ANR’s in $ℝ^n$

Dobrowolski, Tadeusz; Rubin, Leonard

The space of ANR’s in

ℝ^{n}

Dobrowolski, Tadeusz ; Rubin, Leonard

Fundamenta Mathematicae, Tome 144 (1994), p. 31-58 / Harvested from The Polish Digital Mathematics Library

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Résumé

The hyperspaces $A N R (ℝ^{n})$ and $A R (ℝ^{n})$ in $2^{ℝ^{n}} (n \geq 3)$ 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.

Publié le : 1994-01-01

Zbl 0817.54008

EUDML-ID : urn:eudml:doc:212050

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     author = {Tadeusz Dobrowolski and Leonard Rubin},
     title = {The space of ANR's in $$\mathbb{R}$^n$
            },
     journal = {Fundamenta Mathematicae},
     volume = {144},
     year = {1994},
     pages = {31-58},
     zbl = {0817.54008},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv146i1p31bwm}
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Dobrowolski, Tadeusz; Rubin, Leonard. The space of ANR’s in $ℝ^n$
            . Fundamenta Mathematicae, Tome 144 (1994) pp. 31-58. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv146i1p31bwm/

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