  Brodskiy, Dydak, LaBuz, and Mitra introduced the concepts of uniform
joinability and local uniform joinability for uniform spaces when developing
their theory of generalized uniform covering maps which was motivated by a
paper by Berestovskii and Plaut. (Local) uniform joinability can be thought of
as analogous to (local) path connectedness. A chain connected locally uniformly
joinable uniform space is uniformly joinable. This note gives an example of a
metric space that is uniformly joinable but not locally uniformly joinable.
  Plaut recently defined the concept of a weakly chained uniform space. We show
that a weakly chained metrizable uniform space is locally uniformly joinable.
Since local uniform joinability is equivalent to pointed 1-movability for
metric continua, we find that weak chainability is equivalent to pointed
1-movability for such spaces.
