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 García-Ramos (CONACyT & UASLP, Mexico).