We present several results on the compactness of space morphisms between analytic spaces in sense Berkovich. show that under certain conditions source, every sequence maps having an affinoid target has a subsequence converges pointwise to continuous map. also study class arise this way. Locally, they turn be after base change. Our naturally lead definition normal families. give some application...

‎Let $G$ be a finite group and $nu(G)$ denote the number of conjugacy classes of non-normal subgroups of $G$‎. ‎In this paper‎, ‎all nilpotent groups $G$ with $nu(G)=3$ are classified‎.  

Faroldi argues that deontic modals are hyperintensional and thus traditional modal logic cannot provide an appropriate formalization of situations. To overcome this issue, we introduce novel justification logics as analogues to non-normal logics. We establish soundness completeness with respect various models study the problem realization.