Nontrivial topological quandles (Q2101712)

The author shows that there are infinitely many nonisomorphic quandle structures on any topological space \(X\) of positive dimension, thereby presenting a counterexample to Conjecture 5.2 in [\textit{Z. Cheng} et al., Topology Appl. 248, 64--74 (2018; Zbl 1401.57024)] which asserted that there are no nontrivial quandle structures on the closed unit interval \([0,1]\).