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We define an infinite Lyndon word as the limit of an increasing sequence of prefix preserving lyndon words and show that some of the interesting properties of Lyndon words generalize to the infinite case. We construct a queue automaton that recognizes the set of Lyndon words and show that it can be extended to recognize infinite Lyndon words. We discuss certain topological properties of the set of infinite Lyndon words such as homeomorphism with a subspace of the Cantor space.