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Dec 9, 2017 at 21:28 vote accept contemplator
Dec 9, 2017 at 21:27 comment added contemplator Thank you for all your answer. This proof also works. You can also check how our research group came up with the solution.
Dec 4, 2017 at 7:09 comment added Mark Grant @JeffStrom: it looks like you are using a non-standard definition of topological complexity. The standard definition uses covers of $X\times X$, whereas in your answer you find a cover of $X$.
Dec 3, 2017 at 21:21 comment added Jeff Strom This is interesting! My argument is wrong, but I don’t see why.
Dec 3, 2017 at 20:40 history answered Mark Grant CC BY-SA 3.0