© 2002 Springer-Verlag New York Inc. The Alexandroff Dimension of Digital Quotients of Euclidean Spaces

Abstract. Alexandroff T0-spaces have been studied as topological models of the sup-ports of digital images and as discrete models of continuous spaces in theoretical physics. Recently, research has been focused on the dimension of such spaces. Here we study the small inductive dimension of the digital space X.W / constructed in [15] as a minimal open quotient of a fenestrationW ofRn. There are fenestrations ofRn giving rise to digital spaces of Alexandroff dimension different from n, but we prove that ifW is a fenestration, each of whose elements is a bounded convex subset of Rn, then the Alexandroff dimension of the digital space X.W / is equal to n. 1