At present, investigating the issues of the system safety based on barrier functions, such as safety diagnosis, safety control, etc., is mainly to verify the forward invariance of the feasible state set of the system or to ensure the invariance through control means. Such sets are usually static and will not change over time. However, facing practical cases, some systems have performance or state degradation characteristics, and some obstacles in the motion control systems have mobility, and there may be other possibilities. All of these will make us have to consider these feasible state sets are time-varying. To solve the safety control problems caused by this kind of sets with continuous time-varying characteristics, which can be called continuously dynamical sets, this paper is for the first time to discuss two motion modes of the setspace translation and expansion/collapse, and establish the corresponding safety criteria. It is useful to lay the foundation for realizing safety diagnosis and control under one or multiple continuously dynamical sets. At the same time, the paper also verifies the validity of the proposed theory through a few of simple simulation examples.