Infinite simple homotopy types

SummaryTwo finite simplicial complexes have the same simple homotopy type if and only if, when they are embedded in euclidean space of high dimension, their closed regular neighborhoods are pieeewise-linearly homeomorphic. This notion, finer than homotopy type, was analysed by J. H. C. Whitehead [9], [10], [11]. There is a natural extension of this notion to locally finite complexes, which is here analysed with the help of results of Whitehead and C. T. C. Wall