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

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Abstrakt

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.
OriginalsprogEngelsk
UdgivelsesstedAalborg
ForlagDepartment of Mathematical Sciences, Aalborg University
Antal sider8
StatusUdgivet - 2004
NavnResearch Report Series
NummerR-2004-31
ISSN1399-2503

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