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 Mar28 awarded Good Question Jan9 awarded Curious Jan8 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. Jan8 comment Is there a multiple function composition operator? Ah, I seem to have found a duplicate. Unfortunately, the answer seems to be negative. Jan8 revised Is there a multiple function composition operator? added 534 characters in body Jan8 asked Is there a multiple function composition operator? Nov9 suggested rejected edit on Hölder Condition Implying Uniform Convergence Nov9 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. Oct4 awarded Popular Question Sep24 awarded Autobiographer Aug22 awarded Yearling May14 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? May14 accepted What are the minimal conditions for the exactness of a 1-form on an open connected subset? May14 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. May14 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 $\textbf{x}$. May14 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? May14 asked What are the minimal conditions for the exactness of a 1-form on an open connected subset? May10 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? May7 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. May7 comment Prove that an open interval and a closed interval are not homeomorphic Why is $(0,1)$ not compact? Its compactness needs to be evaluated relative to its induced topology, not some unrelated superset like $\mathbb{R}$.