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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 thatthe limit space $N_{\infty} = \varprojlim \mathbf{N}_{\mathcal A}$ is homotopyequivalent to $X$. A connection with cell structures [2],[3] is discussed

Inverse systems with simplicial bonding maps and cell structures