Chaos in countable dynamical system

Let (X,τ) be a countable compact Hausdorff space and let F :X→X be continuous. We investigate the distributional chaos introduced in [B. Schweizer, J. Smı́tal, Trans. Amer. Math. Soc. 344 (1994) 737–754] for the case of a countable dynamical system (X,F).