Abstract
ABSTRACT:We present five examples illustrating that results well known for discrete dynamical systems on (locally) compact metric spaces and continuous functions can fail if either (local) compactness or metrizable is removed. Some samples are: A homeomorphism h from the space ℙ of irrationals to itself such that [ℙ; h] has each point recurrent, but [ℙ; h] has no minimal sets. Commuting homeomorphisms f and g from a compact space X to itself such that [X; f] and [X; g] have no common recurrent points.
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