Bulletin of the
Korean Mathematical Society BKMS

In this paper we characterize asymptotic stability via Lyapunov function in general dynamical systems on c-first countable space. We give a family of examples which have first countable but not c-first countable, also c-first countable and locally compact space but not metric space. We obtain several necessary and sufficient conditions for a compact subset $M$ of the phase space $X$ to be asymptotic stability.

Keywords: C- first countable space, asymptotic stability, general dynamical systems, Lyapunov function and strict Lyapunov function

MSC numbers: 37B25