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About: Locally finite poset     Goto   Sponge   NotDistinct   Permalink

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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.