Decomposition Space Theory and the Bing Shrinking Criterion

‘Decomposition Space Theory and the Bing Shrinking Criterion’ gives a proof of the central Bing shrinking criterion and then provides an introduction to the key notions of the field of decomposition space theory. The chapter begins by proving the Bing shrinking criterion, which characterizes when a given map between compact metric spaces is approximable by homeomorphisms. Next, it develops the elements of the theory of decomposition spaces. A key fact is that a decomposition space associated with an upper semi-continuous decomposition of a compact metric space is again a compact metric space. Decomposition spaces are key in the proof of the disc embedding theorem.