Nicolas
Reputation
Next privilege 250 Rep.
 Jul2 awarded Curious Apr9 comment Sum of closed and compact set in a TVS Would you please explain how you conclude, in the end, that $y=a+b$ should be in $V_{a_i}$ for some $i$ ? I agree that $a \in (V_{a_i} - B)$ for some $i$, but this does not (directly) imply that $a+b \in V_{a_i}$ for some $i$. Feb10 accepted If $X$ is a compact metric space, $Homeo(X)$ is second countable Feb9 asked If $X$ is a compact metric space, $Homeo(X)$ is second countable Jan28 accepted Pointwise convergence to a constant function on a compact space Jan28 comment Pointwise convergence to a constant function on a compact space Thanks a lot for your answer! Your counterexample is indeed simple, but not totally easy to find. I would have prefered an affirmative answer, but that's not your fault :-) Jan26 asked Pointwise convergence to a constant function on a compact space Jun5 accepted Space $H^1([0, T], H^{-1}(U))$ Jun5 comment Space $H^1([0, T], H^{-1}(U))$ Oh yes, I found your definition in Evan's! Thank you :) Jun5 comment Space $H^1([0, T], H^{-1}(U))$ But what would this product between $\varphi'$ and $u$ mean in this context where $X = H^{-1}(U)$? Jun5 revised Space $H^1([0, T], H^{-1}(U))$ edited body Jun5 comment Space $H^1([0, T], H^{-1}(U))$ Oh yeah sorry, I correct it. Jun5 comment Prove/disprove: There isn't any graph with an even number of vertices and an odd number of edges that contains Euler's circuit. Yes, if the graph is connected, you can easily prove the proposition, but if it isn't, your example is correct. Now you have to see if the man who wrote the proposition just forgot the word "connected" or if he is expecting a disconnected example as yours... Jun5 asked Space $H^1([0, T], H^{-1}(U))$ May22 revised Uniform convergence and uniform boundedness added 2 characters in body May22 comment Uniform convergence and uniform boundedness Actually, they say "... is majorised (see p.67) ...", and the definition of majorised is precisely, page 67 : "Let $f$, $F$ be functions with domain in $\mathbb{R}^n$ and range in $\mathbb{R}^m$, of class $C^\infty$ in a neighborhood of the origin. We say $f$ is majorised by $F$, if $|D^\alpha f_k(0)| \leq D^\alpha F_k(0)$ for all $\alpha \in \mathbb{Z}^n$ and all $k$." I suppose that what they mean here is that each term of the series $(*)$ is less than the corresponding term of the series of $U$. We have proved it, as I've just added in my first post. May22 revised Uniform convergence and uniform boundedness added 139 characters in body May21 awarded Commentator May21 comment Uniform convergence and uniform boundedness Sorry but you don't really help me... I've already searched for hours and your hints which are just reformulation of the definition of uniform convergence don't help me a lot. I've succeeded to prove the uniform convergence on every compact, using the boundedness of $U$, I'll do with that. Thank you for your time ;) May21 awarded Editor