  We investigate Problem 155 form the "Scottish Book" due to S. Mazur and L.
Sternbach. In modern terminology they asked if every bijective, locally
isometric map between two real Banach spaces is always a global isometry.
Recently, an affirmative answer when the source space is separable was obtained
by M. Mori, using techniques related to the Mazur-Ulam theorem and its
generalizations. The main purpose of this short note is to offer a different
approach to Problem 155 motivated by recent advances in metric geometry. We
show that it has an affirmative answer under the additional assumption that the
map considered is a local isometry.

Functional Analysis;Metric Geometry