We characterize the closure of the set of iterable functions in the space of all continuous self-mappings of a real compact interval endowed with the supremum norm. A full description of iterable functions was given by M. C. Zdun. The present paper continues the research of �near-embeddability� started by W. Jarczyk, who was inspired by a problem of E. Jen presented by Gy. Targonski, and by the present author.
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