International Journal of Mathematics and Mathematical Sciences
Volume 22 (1999), Issue 3, Pages 611-616
doi:10.1155/S0161171299226117
Tilings in topological spaces
Department of Geometry and Topology, Faculty of Sciences, Universidad de Almería, Almería 04071, Spain
Received 11 September 1996; Revised 6 May 1997
Copyright © 1999 F. G. Arenas. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
A tiling of a topological space X is a covering of X by sets (called tiles) which are the closures of their
pairwise-disjoint interiors. Tilings of ℝ2 have received considerable attention (see [2] for a wealth of interesting examples and results as well as an extensive bibliography). On the other hand, the study of tilings of general topological spaces is just beginning (see [1, 3, 4, 6]). We give some generalizations for topological spaces of some results known for certain classes of tilings of topological vector spaces.