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The topology of the Banach–Mazur compactum

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Antonyan S. A.

Fundamenta Mathematicae

2000

tom 166

nr 3

209-232

Let J(n) be the hyperspace of all centrally symmetric compact convex bodies $A ⊆ \Bbb R^n$, n ≥ 2, for which the ordinary Euclidean unit ball is the ellipsoid of maximal volume contained in A (the John ellipsoid). Let $J_0(n)$ be the complement of the unique O(n)-fixed point in J(n). We prove that: (1) the Banach-Mazur compactum BM(n) is homeomorphic to the orbit space J(n)/O(n) of the natural action of the orthogonal group O(n) on J(n); (2) J(n) is an O(n)-AR; (3) $J_0(2)/SO(2)$ is an Eilenberg-MacLane space $\bold K(\Bbb Q,2)$; (4) $BM_0(2) = J_0(2)/O(2)$ is noncontractible; (5) BM(2) is a nonhomogeneous absolute retract. Other models for BM(n) are established.

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1 Fundamenta Mathematicae

1 Antonyan S. A.

1 2000

Wyniki wyszukiwania

The topology of the Banach–Mazur compactum