Talk:P-Product Metrics on Real Vector Space are Topologically Equivalent

It looks to me like the original author managed to do the hard part of this proof and then got stuck on the easy part, thinking zie had to prove more than was actually necessary. I replaced it with something far simpler that I think does work. However, I would really appreciate if other folks could check that I didn't do something totally stupid. --Dfeuer (talk) 18:32, 15 January 2013 (UTC)


 * There is nowhere where it is shown that $d_r \left({x,y}\right) \ge d_\infty \left({x, y}\right)$, or anything similar, as far as I can see. The step that shows why $d_r \left({x, y}\right) \ge d_{r+1} \left({x, y}\right)$ should be correct. --Anghel (talk) 19:06, 15 January 2013 (UTC)


 * Good point. I don't think that was proved in any of the material I erased either. --Dfeuer (talk) 19:09, 15 January 2013 (UTC)


 * But that follows trivially from the fact that the $n$th root is increasing, doesn't it? I'm thinking the whole proof of the chain of inequalities might well belong on a separate page to which this one need not link. Unless I'm thinking entirely bone-headedly, which is always a possibility. --Dfeuer (talk) 19:15, 15 January 2013 (UTC)


 * Yes, it does. So we just need to add that argument. Good job. --Anghel (talk) 19:34, 15 January 2013 (UTC)