Timeline for Is it reasonable to define `poset homotopy' as a `natural transformation of posets'?

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Apr 12, 2011 at 21:38	comment	added	Timothy Chow		I believe the original reference is McCord, Duke Math. J. 33 (1966), 465-474. Here's another way to say it. There are two ways to get a topological space from a finite poset $P$. First we can simply let the downsets of $P$ (i.e., subsets $I\subseteq P$ such that $x\le y \in I$ implies $x\in I$) be the open sets of a topology on the ground set of $P$. The other way is to let the totally ordered subsets of $P$ define an abstract simplicial complex, and consider some geometric realization. McCord shows that there is a weak homotopy equivalence between these two topological spaces.
Apr 12, 2011 at 9:18	history	answered	Neil Strickland	CC BY-SA 3.0