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The space of ANR’s in $ℝ^n$

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Dobrowolski T., Rubin L. R.

Fundamenta Mathematicae

1994-1995

tom 146

nr 1

31-58

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.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Dobrowolski T.

1 Rubin L. R.

1 1994

Wyniki wyszukiwania

The space of ANR’s in $ℝ^n$