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Covering relation information


The Hasse diagram of the power set of three elements, partially ordered by inclusion.

In mathematics, especially order theory, the covering relation of a partially ordered set is the binary relation which holds between comparable elements that are immediate neighbours. The covering relation is commonly used to graphically express the partial order by means of the Hasse diagram.

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Covering relation

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mathematics, especially order theory, the covering relation of a partially ordered set is the binary relation which holds between comparable elements that...

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Hasse diagram

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a different meaning: the directed acyclic graph obtained from the covering relation of a partially ordered set, independently of any drawing of that graph...

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Covering space

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In topology, a covering or covering projection is a map between topological spaces that, intuitively, locally acts like a projection of multiple copies...

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Directed acyclic graph

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reachability relation as the DAG. It has an edge u → v for every pair of vertices (u, v) in the covering relation of the reachability relation ≤ of the DAG...

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Binary relation

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a binary relation associates elements of one set, called the domain, with elements of another set, called the codomain. A binary relation over sets X...

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Cover

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sets whose union contains each set as a subset Cover, a pair in the covering relation of a partially ordered set, or the greater element in such a pair...

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Graded poset

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order, if x < y then ρ(x) < ρ(y), and The rank is consistent with the covering relation of the ordering, meaning that for all x and y, if y covers x then...

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Weak ordering

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partial cube of moves on weak orderings is the graph describing the covering relation of the face lattice of the permutohedron. For instance, for n = 3...

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Distributive lattice

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and join-irreducible elements. If a lattice is distributive, its covering relation forms a median graph. Furthermore, every distributive lattice is also...

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Converse relation

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binary relation is the relation that occurs when the order of the elements is switched in the relation. For example, the converse of the relation 'child of'...

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Connected relation

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In mathematics, a relation on a set is called connected or complete or total if it relates (or "compares") all distinct pairs of elements of the set in...

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Total relation

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In mathematics, a binary relation R ⊆ X×Y between two sets X and Y is total (or left total) if the source set X equals the domain {x : there is a y with...

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Head covering for Christian women

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Christian head covering, also known as Christian veiling, is the traditional practice of women covering their head in a variety of Christian denominations...

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Total order

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which any two elements are comparable. That is, a total order is a binary relation ≤ {\displaystyle \leq } on some set X {\displaystyle X} , which satisfies...

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Partially ordered set

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pair is comparable. Formally, a partial order is a homogeneous binary relation that is reflexive, antisymmetric, and transitive. A partially ordered set...

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Covering system

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Richard Rado. Covering systems can be used to find primefree sequences, sequences of integers satisfying the same recurrence relation as the Fibonacci...

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Transitive reduction

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acyclic graph that has been constructed in this way, it generates the covering relation of the partial order, which is frequently given visual expression...

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Outline of logic

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Congruence relation Connected relation Converse relation Coreflexive relation Covering relation Cyclic order Dense relation Dependence relation Dependency...

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Glossary of order theory

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relation of an antichain is just the identity relation. Approximates relation. See way-below relation. Antisymmetric relation. A homogeneous relation...

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Religious cosmology

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contemporary with those of Neoplatonism. Gnosticism is an imprecise label, covering monistic as well as dualistic conceptions. Usually the higher worlds of...

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