Remarks on microperiodic multifunctions

‎It is well known that a microperiodic function mapping a topological group into reals‎, ‎which is continuous at some point is constant‎. ‎We introduce the notion of a microperiodic multifunction‎, ‎defined on a topological group with values in a metric space‎, ‎and study regularity conditions implying an analogous result‎. ‎We deal with Vietoris and Hausdorff continuity concepts‎. ‎Stability of microperiodic multifunctions is considered‎, ‎namely we show that an approximately microperiodic multifunction is close to a constant one‎, ‎provided it is continuous at some point‎. ‎As a consequence we obtain stability result for an approximately microperiodic single-valued function.