Using the techniques in topological dynamics, we give a uniform treatment of
Li-Yorke chaos, mean Li-Yorke chaos and distributional chaos for continuous
endomorphisms of completely metrizable groups, and characterize three kinds of
chaos (resp. extreme chaos) in term of the existence of corresponding
semi-irregular points (resp. irregular points). We also apply the results to
the chaos theory of continuous linear operators on Fr\'echet spaces, which
improve some results in the literature.Comment: 50 page