Abstract
Embedding of a topological dynamical system into another is a weaker condition than topological conjugacy between the two topological dynamical systems. In 2000, under the assumption of e-expansive, compact and totally disconnected systems, Shigeo Akashi found a sufficient condition for embedding a topological dynamical system (X,. d, f) into a symbolic dynamical system. The purpose of this paper is to present and prove a necessary and sufficient condition that determines exactly which of the topological dynamical systems can be embedded into symbolic dynamical systems and which ones cannot be. Particularly, Shigeo Akashi's result becomes a special case of this new sufficient condition.
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