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The Alexandroff Dimension of Digital Quotients of Euclidean Spaces

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Abstract

Alexandroff T 0 -spaces have been studied as topological models of the supports 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 fenestration W of R n . There are fenestrations of R n giving rise to digital spaces of Alexandroff dimension different from n , but we prove that if W is a fenestration, each of whose elements is a bounded convex subset of R n , then the Alexandroff dimension of the digital space X(W) is equal to n .

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Received December 6, 1999, and in revised form July 5, 2001, and August 31, 2001. Online publication January 7, 2002.

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Wiederhold, P., Wilson, R. The Alexandroff Dimension of Digital Quotients of Euclidean Spaces. Discrete Comput Geom 27, 273–284 (2002). https://doi.org/10.1007/s00454-001-0065-4

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