John
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 Sep12 comment Typo or additional hypotheses needed in problem 5, p.71 of Bredon's Topology and Geometry? I edited the question. It may be possible that the map you define is not an isomorphism after all. Aug30 comment Is there a cantor set in $\mathbb{R}^{n}-\{0\}$ which intersects every ray from the origin? Very elegant, +1! Aug30 comment Is there a cantor set in $\mathbb{R}^{n}-\{0\}$ which intersects every ray from the origin? Yes, you are absolutely right. I edited the question. Aug27 comment A functional structure on the graph of the absolute value function I think I follow, but just in case, could you clarify what you mean when saying "Lipschitz at $(0,0)$". Aug27 comment “Coordinate functions” on the structure-sheaf definition of a smooth manifold No problem. I edited the question and added some links to questions related to the problems of the section you are reading. I am myself stuck on problem 5 p.71 (see the last link I added at the end of my answer) Aug24 comment Partition of Unity in Spivak's Calculus on Manifolds @Pratyush: I have looked at this more carefully and updated my answer. Aug24 comment “Coordinate functions” on the structure-sheaf definition of a smooth manifold @ Alex P. I edited my answer. I hope it helps. $f_{1}=id$ will not work. Just let $f_{1}$ be any constant function. Aug22 comment “Coordinate functions” on the structure-sheaf definition of a smooth manifold @Alex P. Yes, it is false. I provide an asnwer below. Aug8 comment Functionally structured spaces and manifolds I guess you mean that smooth function $h$ be unique, as $g$ is not assumed smooth. Aug4 comment Nets, dense subsets and continuous maps I think he/she meant $D$. Aug4 comment Nets, dense subsets and continuous maps $f=g$ on $X$? $f$'s domain is $D$. What do you mean? $g$ seems to extend $f$. So I would say that $f=g$ on $D$. But that it does so continuously is not so clear to me. Aug2 comment Upper triangular matrices in $\mathrm{SL}(2,\mathbb{R})$ And that is how it is done. Nice! Aug2 comment Upper triangular matrices in $\mathrm{SL}(2,\mathbb{R})$ Yes, $T$ is clearly non-compact. That is precisely why I am asking. Jul29 comment Counterexample or proof that a certain subset in a topological group is closed Thanks, very nice. Jul29 comment Counterexample or proof that a certain subset in a topological group is closed Of course, if singletons are closed in $X$ then $H$ is closed. But that is not what I am asking is it? In any case I clarified the post above. Jul26 comment Closure of a certain subset in a compact topological group Thanks, +1 to your answer Nov29 comment Is this definition missing some assumptions? This was asked before: math.stackexchange.com/questions/127616/… Nov25 comment Do we need additional assumptions for problem 3-37 (b) in Spivak´s calculus on Manifolds? The definition of integral used in the problem involves partitions of unity and absolute convergence of a certain series, and may not coincide with the usual one. See p.65 of the book. Is that the integral you have in mind? Because you don´t mention partitions of unity at all. Nov25 comment Do we need additional assumptions for problem 3-37 (b) in Spivak´s calculus on Manifolds? I stated the problem exactly as it is the book. I know there is no need for additional asumptions to show that the integral does not exist. Also given the fact that Spivak explicitly says "$f(x)=0$ for $x\not\in$ any $A_{n}$" I am inclined to think that he meant that $n\ge 1$. Nov19 comment Solving problem 3-29 in Spivak´s Calculus on Manifolds without using change of variables I may be mistaken, but isn´t this solution basically a change of variables to cylindrical coordinates?