A space with infinite span and zero surjective span

Topics about continua (compact connected metric spaces) are related to Geometry, Topology and Analysis together, so is the case without compactness (topics about connected metric spaces). Open Problem 11 (No. 438 in J. van Mill and G.M. Reedʹs book, Open Problems in Topology [North-Holland, Amsterdam, 1990]).—Is it true that span is less than or equal to the double of surjective span for each connected metric space?—was originally published in The Houston Problem Book (1986) (Problem 83, dated 1975). This paper will compose a counterexample (a submetric space in the plane R2) to give a negative answer for it.