  For a topologically complete space $X$ and a family of closed covers
$\mathcal A$ of $X$ satisfying a "local refinement condition" and a
"completeness condition," we give a construction of an inverse system $\mathbf{
N}_{\mathcal A}$ of simplicial complexes and simplicial bonding maps such that
the limit space $N_{\infty} = \varprojlim \mathbf{N}_{\mathcal A}$ is homotopy
equivalent to $X$. A connection with cell structures [2],[3] is discussed
