Summary: We introduce here notions of chain recurrent sets, attractors and its basins for general dynamical systems and prove important properties including (i) the chain recurrent set \(CR(f)\) of \(f\) on a metric space \((X, d)\) is the complement of the union of sets \(B(A)-A\) as \(A\) varies over the collection of attractors and (ii) genericity of general dynamical systems.