Abstract:
Alexandro T0-spaces have been studied as topological models of the supports of digital images
and as discrete models of continuous spaces in theoretical physics. In this paper we discuss three di erent
dimension functions for this class of spaces, namely the Alexandro dimension, the Order dimension and the
Krull dimension and we outline a proof of the equality of these dimension functions in this class. The rst of
these is essentially the small inductive dimension well-known in topology, the second has been studied in the
theory of posets while the third has been studied extensively as a dimension function for lattices and rings and
was rst applied to topological spaces by Vinokurov in 1966. Since the category of Alexandro T0-spaces is
known to be isomorphic to the category of posets, these results could be formulated in this latter category as
well.
