International Journal of Mathematics and Mathematical Sciences
Volume 22 (1999), Issue 3, Pages 611-616

Tilings in topological spaces

F. G. Arenas

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.


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 2 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.