On the topology of some hyperspaces of convex bodies associated to tensor norms
Luisa F. Higueras-Monta\~no (1), Natalia Jonard-P\'erez (2) ((1), (2) Departamento de Matem\'aticas, Facultad de Ciencias, Universidad Nacional, Aut\'onoma de M\'exico)

TL;DR
This paper characterizes the topological structure of the space of convex bodies associated with tensor norms, showing it is homeomorphic to a product of a Hilbert cube and Euclidean space, revealing its geometric complexity.
Contribution
It determines the homeomorphism type of the hyperspace of tensorial convex bodies, establishing it as an absolute retract homeomorphic to a Hilbert cube times Euclidean space.
Findings
The space of tensorial convex bodies is an absolute retract.
It is homeomorphic to a product of a Hilbert cube and Euclidean space.
The relation between Banach-Mazur compactum and tensorial convex bodies is analyzed.
Abstract
For every tuple let denote the tensor product of Let us denote by the hyperspace of centrally symmetric convex bodies in endowed with the Hausdorff distance, and by the subset of consisting of the convex bodies that are closed unit balls of reasonable crossnorms on It is known that is a closed, contractible and locally compact subset of The hyperspace is called the space of tensorial bodies. In this work we determine the homeomorphism type of We show that even if…
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