Thomas E.
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 Sep12 revised Why is differential geometry called differential geometry? [Edit removed during grace period] Sep12 answered Why is differential geometry called differential geometry? Sep7 answered Does $V_1,V_2,V_3$ span $R^4$ Jul2 awarded Curious May28 comment Research Area Choice: PDE vs Optimization What type of industry would you like to consider outside of academia? Bear in mind that PDEs are used in finance too. May15 comment How to prove or disprove $P(\overline A) = P(U) - P(A)$ Could you clarify what $P(A)$ stands for? And what exactly do you mean by the statement "$U-A$ implies $A\cap \overline{U}$"? May15 comment Show that if sup{∑|f(a)|}<∞, then {a∈A:f(a) is not zer0} is countable. @user140794: Assume that there are infinitely many $a_{1},a_{2},...\in A$ with $f(a_{k})>\frac{1}{n}$ for all $k\in\mathbb{N}$. Then $\sup_{N\in\mathbb{N}}\sum_{k=1}^{N}f(a_{k})=\infty$, which is a contradiction to your assumption. And note for the last part: for absolutely convergent series the order of terms doesn't affect the sum. May14 answered Show that if sup{∑|f(a)|}<∞, then {a∈A:f(a) is not zer0} is countable. May13 answered Any idea of how to prove this May13 revised Proving that there is no norm for the space of real-valued sequences making it a complete metric space. edited tags May13 comment Geometric meaning of symmetric connection Have you computed both sides of $(2)$ for the Euclidean connection on $\mathbb{R}^{n}$? May13 revised Motivation of vector bundle of a manifold edited tags May13 answered Motivation of vector bundle of a manifold May11 comment Equivalent definitions of vector field @soporhs. You're welcome. I'll gladly answer any questions you might have, but I advice that you try to work the details on your own at first. May11 revised Equivalent definitions of vector field added 84 characters in body May11 comment Equivalent definitions of vector field What definition of $TM$ are you working with? It seems that this answer only opens the usual definition of the tangent space but I can't see how you identify those two definitions of a vector field. May11 answered Equivalent definitions of vector field May11 comment Equivalent definitions of vector field What is your definition of $TM$? May6 comment $\mathbb R$ has the same cardinality of any interval $g$ is not defined at $x=-1$. May6 answered Openess of sets given by equivalence relations in the quotient topology.