2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/101146We introduce the notion of nonevasive reduction, and show that for any monotone poset map $ϕ:P\to P$, the simplicial complex $Δ(P)$ {\tt NE}-reduces to $Δ(Q)$, for any $Q\supseteq{\text{\rm Fix}}ϕ$. As a corollary, we prove that for any order-preserving map $ϕ:P\to P$ satisfying $ϕ(x)\geq x$, for any $x\in P$, the simplicial complex $Δ(P)$ collapses to $Δ(ϕ(P))$. We also obtain a generalization of Crapo's closure theorem.To appear in the International Journal of Mathematics and Mathematical SciencesCombinatoricsAlgebraic Topology57C05; 06A06,57C10text