  Chain distance between points in a metric space is defined as the infimum of
epsilon such that there is an epsilon-chain connecting these points. We call a
mapping of a metric compact into the real line a chain development if it
preserves chain distances. We give a criterium of existence of the chain
development for metric compacts. We prove the diameter of any chain development
of a given compact to be the same iff the compact is countable.

Metric Geometry