International Journal of Mathematics and Mathematical Sciences
Volume 22 (1999), Issue 3, Pages 611-616
doi:10.1155/S0161171299226117

Tilings in topological spaces

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.