We provide a purely topological description of minimal and uniquely
ergodic systems whose unique invariant measure is loosely Bernoulli
and has zero entropy (we call such measure preserving systems loosely
Kronecker). At the heart of our result lies Feldman-Katok continuity,
that is, continuity with respect to the Feldman-Katok pseudometric,
which is a topological counterpart of the pseudometric f-bar on a
symbolic space. The talk is based on a joint work with Felipe
GarcĂa-Ramos (CONACyT & UASLP, Mexico).