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Jan
8
comment Is there a multiple function composition operator?
Thank you for the answer. I'm not $\LaTeX$-ing this assignment (for reasons that are not relevant). It seems that no such notation exists, then? I was hoping someone could have come across something in a paper they read before.
Jan
8
comment Is there a multiple function composition operator?
Ah, I seem to have found a duplicate. Unfortunately, the answer seems to be negative.
Jan
8
revised Is there a multiple function composition operator?
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Jan
8
asked Is there a multiple function composition operator?
Nov
9
suggested rejected edit on Hölder Condition Implying Uniform Convergence
Nov
9
comment Hölder Condition Implying Uniform Convergence
I'm working on the exact same problem (Stein and Shakarchi, Complex Analysis, Ch. 3, Problem 5), and I also don't see why this can be so easily asserted. It's a shame no one answered this yet. I attempted to show as $\epsilon\rightarrow 0^+$ that $g(x\pm i\epsilon)$ is uniformly Cauchy, but this didn't get me anywhere either.
Oct
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May
14
comment What are the minimal conditions for the exactness of a 1-form on an open connected subset?
Yes - I mean they still need to be connected, but the paths from $\textbf{a}$ to $\textbf{x}$ are only parallel to the axes in some open set about $\textbf{x}$. If $n$ such paths exist and have the same integrals, one for each dimension, then do we have exactness?
May
14
accepted What are the minimal conditions for the exactness of a 1-form on an open connected subset?
May
14
comment Is there a way in matrix math notation to show the 'flip up-down', and 'flip left-right' of a matrix?
@Spacey no - nothing widely used.
May
14
comment What are the minimal conditions for the exactness of a 1-form on an open connected subset?
I see. Could you please clarify what the minimal condition for exactness is then? It seems that all that's needed is that for every $\textbf{a},\textbf{x}$, that there really only need to be $n$ paths with equivalent integrals, one for each dimension, where the paths don't even need to trace out $\partial\Delta$ fully, but just near $\textbf{x}$.
May
14
comment Is there a way in matrix math notation to show the 'flip up-down', and 'flip left-right' of a matrix?
For a matrix $M$, will $DM$ and $MD$ suffice for up-down and left-right flips, respectively, where $D$ is the unit anti-diagonal matrix?
May
14
asked What are the minimal conditions for the exactness of a 1-form on an open connected subset?
May
10
comment Why does $\exists x\,\ x = x$?
@RickyDemer So, basically, the difference between your formalization and the one in Wikipedia is that there's an additional existential qualifier $\exists\emptyset$ in the Axiom of Infinity?
May
7
comment Prove that an open interval and a closed interval are not homeomorphic
Right, it should be the induced topology. What I'm saying is that it isn't clear that on the induced topology that the whole unit open interval is not a compact set. On the induced topology it is closed after all.