Houston Problem Book Problem 58

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Problem 58 (HPB): Suppose $f$ is a continuous mapping of a chainable continuum $X$ onto a nonchainable continuum $Y$. Does there exist a subcontinuum $X'$ of $X$ mapped onto $Y$ under $f$ such that $f \big|_{X'}$ is not weakly confluent? (Asked by A. Lelek 25 January 1981)

Answer: No (T. Maćkowiak and E.D. Tymchatyn 25 January 1981)