Locally finite poset

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.
References.
Stanley, Richard P. Enumerative Combinatorics, Volume I. Cambridge University Press, 1997. Pages 98, 113–116.