Lelek’s problem is not a metric problem. (English summary) Topology Appl. 158 (2011), no. 18, 2479–2484. Summary: “We show that Lelek’s problem on the chainability of continua with span zero is not a metric problem: from a non-metric counterexample one can construct a metric one.
10. A. Lelek, On the surjective span and semispan of connected metric spaces, Colloq. Math. 37
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