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Nov 18, 2015 at 17:42 history edited Sebastian Goette CC BY-SA 3.0
integrated answer to http://mathoverflow.net/q/223925/70808
Nov 18, 2015 at 13:56 comment added Julian Newman I've just asked my new question: mathoverflow.net/questions/223925/…
Nov 18, 2015 at 13:07 comment added Julian Newman Thank you; I certainly wasn't just going to replace my original question with the new one. Having your answer to my current version of the problem is by no means irrelevant for me.
Nov 18, 2015 at 4:50 comment added Julian Newman Thank you very much for this. Now since posting the question, I've come to realise that for the problem I'm working on, I should take the sets $V_1,\ldots,V_n$ to be not just connected, but actually homeomorphic to $\mathbb{R}^d$! Do you have any thoughts as to whether, under this additional constraint, a vector $\mathbf{v} \in \mathbb{R}^d$ with the stated property can exist (with $d \geq 3$)? [Or maybe I should post this as a new MathOverflow question?]
Nov 18, 2015 at 4:45 vote accept Julian Newman
Nov 17, 2015 at 21:59 history edited Sebastian Goette CC BY-SA 3.0
Now, a complete answer.
Nov 17, 2015 at 18:46 history edited Sebastian Goette CC BY-SA 3.0
edited body
Nov 17, 2015 at 18:40 history answered Sebastian Goette CC BY-SA 3.0