Locally finite poset (original) (raw)
In mathematics, a locally finite poset is a partially ordered set P such that for all x, y ∈ P, the interval [x, y] consists of finitely many elements. Given a locally finite poset P we can define its incidence algebra. Elements of the incidence algebra are functions ƒ that assign to each interval [x, y] of P a real number ƒ(x, y). These functions form an associative algebra with a product defined by There is also a definition of incidence coalgebra. In theoretical physics a locally finite poset is also called a causal set and has been used as a model for spacetime.
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| dbo:abstract | In mathematics, a locally finite poset is a partially ordered set P such that for all x, y ∈ P, the interval [x, y] consists of finitely many elements. Given a locally finite poset P we can define its incidence algebra. Elements of the incidence algebra are functions ƒ that assign to each interval [x, y] of P a real number ƒ(x, y). These functions form an associative algebra with a product defined by There is also a definition of incidence coalgebra. In theoretical physics a locally finite poset is also called a causal set and has been used as a model for spacetime. (en) Em matemática, um conjunto parcialmente ordenado localmente finito é um conjunto parcialmente ordenado P parcialmente ordenado tal que para todo x, y ∈ P, o intervalo [x, y] consiste em elementos finitos. Dado um poset localmente finito P podemos definir sua incidência álgebra. Elementos da álgebra de incidência são funções ƒ que atribuem a cada intervalo [x, y] de P um número real ƒ (x, y). Estas funções formam uma álgebra associativa com produto definido por Há também uma definição de "coálgebra de incidência", e na física teórica, um conjunto parcialmente ordenado localmente finito é também chamado de conjunto causal e tem sido usado como um modelo para o espaço-tempo granular. (pt) |
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| rdfs:comment | In mathematics, a locally finite poset is a partially ordered set P such that for all x, y ∈ P, the interval [x, y] consists of finitely many elements. Given a locally finite poset P we can define its incidence algebra. Elements of the incidence algebra are functions ƒ that assign to each interval [x, y] of P a real number ƒ(x, y). These functions form an associative algebra with a product defined by There is also a definition of incidence coalgebra. In theoretical physics a locally finite poset is also called a causal set and has been used as a model for spacetime. (en) Em matemática, um conjunto parcialmente ordenado localmente finito é um conjunto parcialmente ordenado P parcialmente ordenado tal que para todo x, y ∈ P, o intervalo [x, y] consiste em elementos finitos. Dado um poset localmente finito P podemos definir sua incidência álgebra. Elementos da álgebra de incidência são funções ƒ que atribuem a cada intervalo [x, y] de P um número real ƒ (x, y). Estas funções formam uma álgebra associativa com produto definido por (pt) |
| rdfs:label | Locally finite poset (en) Conjunto parcialmente ordenado localmente finito (pt) |
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