By tiling of a normed space we mean a covering of it by proper subsets that are the closure of their nonempty connected pairwise disjoint interiors. In the literature, only starting with the eighties attention has been payed to tilings in the infinite-dimensional context: the related theory already contains some remarkable results, but still appears widely incomplete. Here we present the state of the art, by discussing separately two fundamental aspects of the subject, the global one and the local one.
Even infinite-dimensional Banach spaces can enjoy carpeting and tiling / C. Zanco - In: Proceedings of the 13th. Seminar on Analysis and Its Applications / S. Azam, S. Nobakhtian, M.R. Pouryayevevali, A. Rejali, G. Vakili, J. Zafarani. - [s.l] : Isfahan University Press, 2003. - ISBN 964-8658-02-1. - pp. 121-141 (( Intervento presentato al 13. convegno Even in13th. Seminar on Analysis and Its Applications tenutosi a Isfahan (Iran) nel 2003.
Even infinite-dimensional Banach spaces can enjoy carpeting and tiling
C. ZancoPrimo
2003
Abstract
By tiling of a normed space we mean a covering of it by proper subsets that are the closure of their nonempty connected pairwise disjoint interiors. In the literature, only starting with the eighties attention has been payed to tilings in the infinite-dimensional context: the related theory already contains some remarkable results, but still appears widely incomplete. Here we present the state of the art, by discussing separately two fundamental aspects of the subject, the global one and the local one.
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