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 2d comment Hill climbing extremist Walner, Any progress? Do you have an example for me which shows that it is not possible? Nov 19 comment Hill climbing extremist Imagine single hill. In order to get from point A to point B, you go straight uphill and you get on the top of this hill then you go downhill in the direction you would come from if you started in the point B, in this way you get to point B. Such a path is not an integral curve of that vector field. Nov 19 comment Hill climbing extremist Sorry but I can't figure out your idea. Please give me a counterexample which satisfies my conditions, than I will be happy, but now I do not find your answer helpful. I believe that you still misunderstand my question, have in mind following simple example: Nov 18 comment Hill climbing extremist And important thing is that I'm not looking for integral curves of some vector field, because you cannot get into point, where the field is zero, in finite time(vector field has to be lipschitz). But in my question such a points play very important role. Nov 18 comment Hill climbing extremist Sorry I had to down vote. Your answer is not helpfull in any way. Your 'counter example' is the exact reason why $\phi$ has to be zero at infinity. The variational formulation does not make any sense. Constant paths minimizies the integral or paths that are perpendicular to the $\nabla \phi$. I'm not interested in such paths. Nov 17 awarded Nice Question Nov 17 answered Evaluate limit $\displaystyle\lim_{x\rightarrow\infty} (1+\sin{x})^{\frac{1}{x}}$ Nov 15 answered Does there exist a continuous $g(x,t)$ such that every continuous$f(x)$ equals $g(x,t)$ for some $t$ and all $x$?? Nov 14 reviewed Approve The graph of $f$ is a connected subset of $\mathbb{R}^2$. Nov 13 awarded Mortarboard Nov 13 awarded Good Answer Nov 13 asked Hill climbing extremist Nov 12 reviewed Approve What software can draw pictures like this? Nov 12 awarded Nice Answer Nov 12 answered What software can draw pictures like this? Sep 21 revised Understanding commutative cochain problem added 477 characters in body Sep 21 comment Understanding commutative cochain problem Ups, I have a little knowledge of the math in question, so I'm probably mixing up terminology. Ok, what is the difference between simplicial chain complex(scc) and simplicial complex(sc)? Is it that all simplices in scc have fixed orientation? Why is there a problem for simplicial chain complex to be subcomplex of another ordinary chain complex? Scc is an ordinary chain complex right? And yes, ordinary simplicial cochains form a dga, which is not graded-commutative but I'm looking for graded-commutative dga. I changed dga to dgca in the question to make it more clear. Sep 21 revised Understanding commutative cochain problem added 2 characters in body Sep 17 asked Understanding commutative cochain problem Sep 13 comment Is $C^{\infty}(\mathbb{T})$ dense in $C(\mathbb{T})$? What is $\mathbb{T}$? And what is smooth function on general topological space? Or is $X$ manifold?