A NOTE ON SIMPLICIAL COLLAPSING

In this paper we will let $L$ denote a simplicial complex, $K$ a $sub\omega lnplex$ of $L,$ $S^{ll}$ a simplicial complex consisting of all $j$-simplexes of an $n+1$ simplex, $i\leqq n$ , and $S^{1l}K$ the simplicial $\omega mplex$ which is the join of $S^{n}$ and $K$. We denote the $r$-th derived subdivision of $L$ by $L^{(\gamma)}$ and denote a simplicial collapse of $L$ onto $K$ by $L\backslash _{\lrcorner}K[1]$ .