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TILING INFINITE-DIMENSIONAL NORMED SPACES
Published online by Cambridge University Press: 01 November 1997
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).
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- © The London Mathematical Society 1997
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