Approximate inverse systems of compacta and covering dimension (Q1094699)

Approximate inverse systems of metric compacta are introduced and studied. The bonding maps in these systems commute only up to certain controlled values. With every such system \(X=(X_ a,\epsilon _ a,p_{aa'},A)\) are associated a limit space X and projection \(p_ a:X\to X_ a\). A compact Hausdorff space X has covering dimension dim \(X\leq n\) if and only if it can be obtained as the limit of an approximate inverse system of compact polyhedra of dimension \(\leq n\). The analogous statement for usual inverse systems is known to be false.