Abstract
In [F. Zhang, R. Qiu and Y. Zou, The subset of [Formula: see text] realizing metrics on the curve complex, Topology Appl. 193 (2015) 259–269], they defined a subset [Formula: see text] of [Formula: see text] and a metric [Formula: see text] through each point of [Formula: see text] for the curve complex [Formula: see text]. For further understanding the curve complex, we concern the whole set [Formula: see text]. With adaption to the flow theory on torus, we prove that for any point of [Formula: see text], the [Formula: see text] is not a metric on [Formula: see text] or [Formula: see text]. This means that the [Formula: see text] is the maximal subset of [Formula: see text] realizing metrics on the curve complex.
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