Cubical local partial orders on cubically subdivided spaces - existence and construction

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Abstract

The geometric models of Higher Dimensional Automata and Dijkstra's PV-model are cubically subdivided topological spaces with a local partial order. If a cubicalization of a topological space is free of immersed cubic Möbius bands, then there are consistent choices of direction in all cubes, such that any n-cube in the cubic subdivision is dihomeomorphic to [0,1]^n with the induced partial order from R^n. After subdivision once, any cubicalized space has a cubical local partial order. In particular, all triangularized spaces have a cubical local partial order. This implies in particular that the underlying geometry of an HDA may be quite complicated.
Original languageEnglish
Place of PublicationAalborg
PublisherDepartment of Mathematical Sciences, Aalborg University
Number of pages8
Publication statusPublished - 2004
SeriesResearch Report Series
NumberR-2004-31
ISSN1399-2503

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