An abstract polytope is a partially ordered set ( poset ) of elements whose partial ordering obeys certain rules of incidence ( connectivity ) and ranking.
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The standard definition proceeds via transfinite induction and the ordering ( a partial ordering of Kleene's \ mathcal { O } ) is defined simultaneously.
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*PM : partial ordering in a topological space, id = 8775 new !-- WP guess : partial ordering in a topological space-- Status:
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*PM : partial ordering in a topological space, id = 8775 new !-- WP guess : partial ordering in a topological space-- Status:
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Together with Colin Fidge, he developed the vector clock algorithm, which allows to generate a partial ordering of events in a distributed system and to detect causality violations.
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The faces of a convex polytope thus form an lattice called its "'face lattice "', where the partial ordering is by set containment of faces.
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The set of all topologies on a set " X " together with the partial ordering relation ?" forms a complete lattice that is also closed under arbitrary intersections.
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Dependency graphs without circular dependencies form directed acyclic graphs, representations of partial orderings ( in this case, across a spreadsheet ) that can be relied upon to give a definite result.
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Balaban and Klein have more recently proposed a diagram showing partial ordering of sciences in which chemistry may be argued is the central science since it provides a significant degree of branching.
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At the time the idiom was introduced ( 1994 ) the C + + language did not define a partial ordering for overloaded function templates and as a result overloading function templates often resulted in ambiguities.
