On the topology of the chain recurrent set of a dynamical system
Keywords:chain recurrent, chain transitive, chain component, inverse limit space.
Abstractn this paper we associate a pseudo-metric to a dynamical system on a compact metric space. We show that this pseudo-metric is identically zero if and only if the system is chain transitive. If we associate this pseudo-metric to the identity map, then we can present a characterization for connected and totally disconnected metric spaces.
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