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 Aug 30 answered is $\{(x,y) : x,y \in \mathbb{Z} \}$ a closed set? Aug 28 awarded Nice Answer Aug 27 accepted A functional structure on the graph of the absolute value function Aug 27 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 $(0,0)$". Aug 27 revised “Coordinate functions” on the structure-sheaf definition of a smooth manifold Added links Aug 27 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) Aug 24 comment Partition of Unity in Spivak's Calculus on Manifolds @Pratyush: I have looked at this more carefully and updated my answer. Aug 24 revised Partition of Unity in Spivak's Calculus on Manifolds Clarification of ideas Aug 24 revised Partition of Unity in Spivak's Calculus on Manifolds Clarification Aug 24 answered Partition of Unity in Spivak's Calculus on Manifolds Aug 24 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. Aug 24 revised “Coordinate functions” on the structure-sheaf definition of a smooth manifold Additional explanation Aug 22 asked $n\times n$ matrix with zero determinant? Aug 22 comment “Coordinate functions” on the structure-sheaf definition of a smooth manifold @Alex P. Yes, it is false. I provide an asnwer below. Aug 22 answered “Coordinate functions” on the structure-sheaf definition of a smooth manifold Aug 22 revised Typo or additional hypotheses needed in problem 5, p.71 of Bredon's Topology and Geometry? Word change Aug 22 awarded Cleanup Aug 22 revised Typo or additional hypotheses needed in problem 5, p.71 of Bredon's Topology and Geometry? rolled back to a previous revision Aug 22 revised Typo or additional hypotheses needed in problem 5, p.71 of Bredon's Topology and Geometry? Title change Aug 22 revised Typo or additional hypotheses needed in problem 5, p.71 of Bredon's Topology and Geometry? Progress posted and help seeking