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TILING INFINITE-DIMENSIONAL NORMED SPACES

Published online by Cambridge University Press:  01 November 1997

V. FONF ,
A. PEZZOTTA  and
C. ZANCO
V. FONF
Affiliation:
Department of Mathematics, Ben-Gurion University of the Negev, P.O. Box 653, Beer-Sheva 84105, Israel
A. PEZZOTTA
Affiliation:
Dipartimento di Matematica ‘F. Enriques’, Universita' degli Studi, Via C. Saldini, 50, 20133 Milano Mi, Italy
C. ZANCO
Affiliation:
Dipartimento di Matematica ‘F. Enriques’, Universita' degli Studi, Via C. Saldini, 50, 20133 Milano Mi, Italy
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Abstract

The present paper deals with real infinite-dimensional normed spaces; some of the main concepts here make sense, and have been treated in the literature, in the general context of topological Hausdorff linear spaces over reals.

A subset of a normed space X is a body if it is different from X itself and is the closure of its non-empty interior. A covering of X by bodies is called a tiling ofX whenever any two different members of it have disjoint interiors. The elements of such a covering are called tiles. A tiling is bounded (respectively convex) whenever each tile is bounded (respectively convex).

Type
Research Article
Information
Bulletin of the London Mathematical Society , Volume 29 , Issue 6 , November 1997 , pp. 713 - 719
Copyright
© The London Mathematical Society 1997

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