- Tytuł:
- The topology of the Banach–Mazur compactum
- Autorzy:
- Antonyan, Sergey
- Powiązania:
- https://bibliotekanauki.pl/articles/1204942.pdf
- Data publikacji:
- 2000
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
Banach-Mazur compactum
G-ANR
orbit space
Q-manifoldhomotopy type
Eilenberg-MacLane space $\bold K(\Bbb Q,2)$ - Opis:
- Let J(n) be the hyperspace of all centrally symmetric compact convex bodies $A ⊆ \mathbb{R}^n$, 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 $\bb K(\mathbb{Q},2)$; (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.
- Źródło:
-
Fundamenta Mathematicae; 2000, 166, 3; 209-232
0016-2736 - Pojawia się w:
- Fundamenta Mathematicae
- Dostawca treści:
- Biblioteka Nauki
Artykuł