An explanatory hypothesis for the preconceptions suggests that they are hard-wired. Awareness of the intuitive topological preconceptions could assist the topology teacher. One reasons from the principle that if there is a border, this normally implies that the two sides separated by the border are such that one cannot reach one of them from the other without crossing the border. Once you are on one side, it seems, the border bounds you to that side. Exposure to some topological science does not, by itself, correct one's propensity to misjudge some topological facts.
Double toruses are surprising too.
The equivalence between the object represented in fig. An elastic pince-nez and that represented in fig. 2 Fig. 2. Pince-nez, with interlocking frames. Subjects' understanding of Newtonian physics is blocked by their implicit relying on an intuitive physics which in many cases is at odd with Newtonian physics.