Inverse systems with simplicial bonding maps and cell structures

Abstract

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 $N_{\infty }=\underleftarrow{\lim }{\mathbf{N}}_{\mathcal{A}}$ is homotopy equivalent to $X$. A connection with cell structures [2],[3] is discussed