# Qfwfq

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## Registered User

 Name Qfwfq Member for 3 years Seen 2 hours ago Website Location Age
(formerly user "unknowngoogle", and for a very short time "red herring" but that was a red herring)
 1d comment Hartogs Theorem and Canonical Bundles(continued) See: Fritzsche, Grauert, From holomorphic functions to complex manifolds, Theorem 6.12. 1d comment Hartogs Theorem and Canonical BundlesHartogs' theorem is always misattributed: the one in the OP is Riemann's extension theorem (extension through analytic subsets of codimension $\geq 2$). Hartogs' is about extending through compact subsets. 2d comment Why is Set, and not Rel, so ubiquitous in mathematics?@Wlodzimierz Holsztynski: is the historical reconstruction you hint at based on some objective documents, or is it just a conjecture? 2d comment Why is Set, and not Rel, so ubiquitous in mathematics?@mbsq: (continued) Codomain is very important in the everyday treatement of functions, otherwise you wouldn't be able to conveniently express "surjectivity": we want to be able to neatly express -say- that an operator between Hilbert spaces has dense range (note that the range may not be a complete inner product space) but is not surjective. 2d comment Why is Set, and not Rel, so ubiquitous in mathematics?@mbsq: I think the identification of functions with their graphs, which is prevalent in Logic I presume for practical reasons (you just say $f\subseteq g$ to express that "$g$ is an extension of $f$"), doesn't reflect the mathematical practice, in which a function is actually a triple $(f,\mathrm{dom}(f),\mathrm{cod}(f))$. May11 revised para-complex structuredeleted 4 characters in body May8 comment Functional equationsThe question would be more interesting if we knew what motivates it... Apr25 revised Is there an algebra for divergent series summation operators?deleted 1 characters in body Apr25 comment Does Physics need non-analytic smooth functions?@Zsbán: I don't agree, as this is intended to be a mathematical question (a question in mathematical physics, if you want). +1 for the xkcd quote! ;) Apr24 awarded ● Favorite Question Apr24 awarded ● Notable Question Apr4 comment Infinite dimensional algebraic geometryIf I remember correctly, in the book "Infinite Grassmannians and moduli spaces of G-bundles" by S.Kumar there's a chapter or at least a paragraph on Ind-varieties. Mar30 asked What’s the name of “twisted semidirect products”? Mar27 revised Applications of n-dimensional crystallographic groupsdeleted 23 characters in body Mar18 awarded ● Yearling Mar11 comment Applications of n-dimensional crystallographic groupsThanks Gerry M. for correcting the typos - it was late here and I typed too hastily. Mar10 asked Applications of n-dimensional crystallographic groups Mar7 awarded ● Good Question Mar6 revised Fundamental domain for subgroup of fuchsian Schottky group.edited title Mar1 revised A little question on certain parallel-lines-preserving mapsedited tags Mar1 revised A little question on certain parallel-lines-preserving mapsadded 77 characters in body; added 36 characters in body Mar1 comment A little question on certain parallel-lines-preserving mapsThanks Misha, I was not aware of that '800 classical result. Mar1 asked A little question on certain parallel-lines-preserving maps Feb28 comment Research level applications of “row rank = column rank”?(I took the liberty of editing the title because, adding the " " ) Feb28 revised Research level applications of “row rank = column rank”?edited title Feb27 awarded ● Favorite Question Feb24 comment Undecidability and holomorphic functions (Reference request)@AdamEpstein: amazon.com/… (I'm quite sure F. Di Biase has obtained some results related to my question; actually, I'm not sure if also the work with Krantz had some "undecidability" aspects) Feb24 comment Undecidability and holomorphic functions (Reference request)@AdamEpstein: amazon.it/Fatou-Type-Theorems-Functions-ebook/dp/… Feb23 revised Why is it important that partial derivatives commute?edited body Feb22 comment Understanding Adjointness of Sheaves in Algebraic GeometryIn the last sentence: is it the germ ($\in$ the stalk $\mathcal{G}_x$) or the "value" ($\in$ the fiber $\mathcal{G}\otimes_{\mathcal{O_Y}} \kappa (x)$)? Feb20 asked Undecidability and holomorphic functions (Reference request) Feb17 comment Vector bundles vs principal $G$-bundlesI think you meant " vector bundle associated with [...]", not " $G$-bundle associated with [...]". Feb17 comment Alternate definition of vector bundle?@Martin: a morphism is a map $f: E\to F$ over $B$ such that for every $p\in B$, for every $\alpha$ of a covering that trivializes both bundles, the map $\phi_{\alpha}^F \circ f|_{E_p} \circ (\phi_{\alpha}^E)^{-1} : \mathbb{R}^k \to \mathbb{R}^k$, with the obvious notations, is linear. Are there problems with this definition? Feb16 awarded ● Notable Question Feb15 revised excision in algebraic de Rham cohomologyadded 1 characters in body; added 2 characters in body Feb15 comment Using schemes to prove things about ringsWhy do you apologize for asking a big list question? Feb15 comment Alternate definition of vector bundle?For me the usual definition of vector bundle is: you have diffeomorphisms $\phi:\pi^{-1}(U_{\alpha}) \to U_{\alpha} \times \mathbb{R}^k$ over $U_{\alpha}$, where { $U_{\alpha}$ } is a covering of $B$, and the transition functions $\phi_{\beta} \circ \phi_{\alpha}^{-1} : U_{\alpha\beta} \times \mathbb{R}^k\to U_{\alpha\beta}\times\mathbb{R}^k$ over $U_{\alpha \beta}=U_{\alpha}\cap U_{\beta}$ are fiberwise linear maps. Feb14 awarded ● Popular Question Feb8 comment Why is Set, and not Rel, so ubiquitous in mathematics?@Mariano: LoL, I now understand your comment - I didn't re-read my own question carefully enough! Edited. Now I hope the first sentence sounds less circular :) Feb8 revised Why is Set, and not Rel, so ubiquitous in mathematics?deleted 4 characters in body Feb8 comment Is a variety of algebras a set?I don't understand the question. If $A$ is an algebra in the "variety" deined by $\mathfrak{F}$, then each $A \times \{ \alpha \}$ is in the same variety, for all $\alpha \in \mathsf{Ord}$. Feb8 awarded ● Good Question Feb7 comment Why is Set, and not Rel, so ubiquitous in mathematics?@Ronnie Brown: maybe a modern way to conceptualize partial-function solutions of ODEs and PDEs is just sheaf theory. If the "sheaf of local solutions" of a differential operator is taken as a subsheaf of the sheaf of germs of continuous/smooth/analytic functions, it allows you to express that the solutions vary continuously/smoothy/analytically etc. Feb7 comment Why is Set, and not Rel, so ubiquitous in mathematics?Another question could be: $\mathsf{Set}$ is to a general topos as $\mathsf{Rel}$ is to what structure? Feb7 comment Why is Set, and not Rel, so ubiquitous in mathematics?* Typo: "[...] a Yoneda's lemma for Rel Wich is about [...]" should read "[...] a Yoneda's lemma for Rel is about [...]" in the above comment. Feb7 comment Why is Set, and not Rel, so ubiquitous in mathematics?@DanielMoskovich: Yoneda's lemma states that there's a fully faithful embedding of a category $\mathcal{C}$ into the category $\mathsf{Cat}(\mathcal{C}^{\mathrm{op}},\mathsf{Set})$. Perhaps a Yoneda's lemma for Rel Which is about the relationship between $\mathcal{C}$ and $\mathsf{Cat}(\mathcal{C}^{\mathrm{op}},\mathsf{Rel})$, or maybe something less naif. Also, simplicial sets are objects of $\mathsf{Set}^\Delta$; what about $\mathsf{Rel}^\Delta$? Feb7 comment Why is Set, and not Rel, so ubiquitous in mathematics?Thanks for editing the title. Feb7 awarded ● Nice Question Feb7 asked Why is Set, and not Rel, so ubiquitous in mathematics? Feb6 comment Ring with three binary operations@NoahStein: appearently, one cannot have too much "distributivity": see my answer about Eckmann-Hilton theorem.