Guilherme Freitas
Reputation
Next privilege 100 Rep.
Edit community wikis
 Nov 6 awarded Supporter Oct 23 answered More Theoretical and Less Computational Linear Algebra Textbook Oct 23 comment Show that a function that is locally increasing is increasing? Adding to coffeemath's point: remember the property (maybe definition, depends how you go about it) of compact sets in $\mathbb{R}$ that "every open covering has a finite subcovering". That should allow you to "globalize" the local statement. Oct 23 revised Comparison of nonlinear system solvers? Expand on the previous answer. Oct 23 revised Question regarding Kuhn-Tucker multiplier added 361 characters in body Oct 23 revised Why is it that $\mathbb{Q}$ cannot be homeomorphic to _any_ complete metric space? Clarify where the supplied "proof" fails, based on the comments. Oct 23 revised Question regarding Kuhn-Tucker multiplier Cleanup. I cannot understand what is being asked in item (c). Oct 23 answered Question regarding Kuhn-Tucker multiplier Oct 23 suggested approved edit on Question regarding Kuhn-Tucker multiplier Oct 23 revised Why is it that $\mathbb{Q}$ cannot be homeomorphic to _any_ complete metric space? THERE WAS A MISTAKE IN THE PROOF. Giving proper credit in the main post. Oct 23 comment Why is it that $\mathbb{Q}$ cannot be homeomorphic to _any_ complete metric space? Agreed. Bit by the "yeah... this should be obvious". My mistake was when I wrote "and more importantly, that $\lim z_{m} = 0$", because, for example the numbers $d(h(y_{m+p}), h(y_{m})$ may be constant (for all positive integers $p$). Counterexamples have already been mentioned (thanks, Asaf, Nate). More explicitly: in my setup, if $Y = (-1, 1)$, $X = \mathbb{R}$ and $h^{-1}(x) = \frac{x}{1+|x|}$, then setting $x_{n} = n$ and $y_{n} = h^{-1}(x_{n})$, we obtain $y_n$ that increases monotonically towards 1, and is thus Cauchy. But $x_{n}$ is not Cauchy, by construction. Thanks, guys. Oct 23 comment Why is it that $\mathbb{Q}$ cannot be homeomorphic to _any_ complete metric space? Sorry, I didn't know about the 5min to comment rule. I'll reply shortly. Oct 23 comment Why is it that $\mathbb{Q}$ cannot be homeomorphic to _any_ complete metric space? > Homeomorphism is not necessarily an isometry. Oct 23 awarded Revival Oct 23 awarded Editor Oct 23 revised Why is it that $\mathbb{Q}$ cannot be homeomorphic to _any_ complete metric space? Giving some intuition before the proof. Oct 23 answered Why is it that $\mathbb{Q}$ cannot be homeomorphic to _any_ complete metric space? Oct 23 awarded Teacher Oct 23 answered Are the Karush-Kuhn-Tucker conditions applicable when one or more of the constraints are nonlinear? Oct 23 answered Comparison of nonlinear system solvers?