Houston Problem Book Problem 1

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Problem 1 (HPB): Suppose $X$ is a continuum which cannot be embedded in any continuum $Y$ such that $Y$ is the union of a countable family of arcs. Does $X$ contain a connected subset that is not path connected? (Asked by E.D. Tymchatyn, 09/30/81)

Answer: No (E.D. Tymchatyn, 09/30/81).