TY - RPRT

T1 - Cubical local partial orders on cubically subdivided spaces - existence and construction

AU - Fajstrup, Lisbeth

PY - 2004

Y1 - 2004

N2 - 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.

AB - 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.

M3 - Report

T3 - Research Report Series

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

PB - Department of Mathematical Sciences, Aalborg University

CY - Aalborg

ER -