Inverse systems with simplicial bonding maps and cell structures

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

Categories: math.GN