Qfwfq

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Name	Qfwfq
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(formerly user "unknowngoogle", and for a very short time "red herring" but that was a red herring)

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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 Bundles Hartogs' 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 $(f,\mathrm{dom}(f),\mathrm{cod}(f))$.
May 11	revised	para-complex structure deleted 4 characters in body
May 8	comment	Functional equations The question would be more interesting if we knew what motivates it...
Apr 25	revised	Is there an algebra for divergent series summation operators? deleted 1 characters in body
Apr 25	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! ;)
Apr 24	awarded	● Favorite Question
Apr 24	awarded	● Notable Question
Apr 4	comment	Infinite dimensional algebraic geometry If 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.
Mar 30	asked	What’s the name of “twisted semidirect products”?
Mar 27	revised	Applications of n-dimensional crystallographic groups deleted 23 characters in body
Mar 18	awarded	● Yearling
Mar 11	comment	Applications of n-dimensional crystallographic groups Thanks Gerry M. for correcting the typos - it was late here and I typed too hastily.
Mar 10	asked	Applications of n-dimensional crystallographic groups
Mar 7	awarded	● Good Question
Mar 6	revised	Fundamental domain for subgroup of fuchsian Schottky group. edited title
Mar 1	revised	A little question on certain parallel-lines-preserving maps edited tags
Mar 1	revised	A little question on certain parallel-lines-preserving maps added 77 characters in body; added 36 characters in body
Mar 1	comment	A little question on certain parallel-lines-preserving maps Thanks Misha, I was not aware of that '800 classical result.
Mar 1	asked	A little question on certain parallel-lines-preserving maps
Feb 28	comment	Research level applications of “row rank = column rank”? (I took the liberty of editing the title because, adding the " " )
Feb 28	revised	Research level applications of “row rank = column rank”? edited title
Feb 27	awarded	● Favorite Question
Feb 24	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)
Feb 24	comment	Undecidability and holomorphic functions (Reference request) @AdamEpstein: amazon.it/Fatou-Type-Theorems-Functions-ebook/dp/…
Feb 23	revised	Why is it important that partial derivatives commute? edited body
Feb 22	comment	Understanding Adjointness of Sheaves in Algebraic Geometry In the last sentence: is it the germ ($\in$ the stalk $\mathcal{G}_x$) or the "value" ($\in$ the fiber $\mathcal{G}\otimes_{\mathcal{O_Y}} \kappa (x)$)?
Feb 20	asked	Undecidability and holomorphic functions (Reference request)
Feb 17	comment	Vector bundles vs principal $G$-bundles I think you meant " vector bundle associated with [...]", not " $G$-bundle associated with [...]".
Feb 17	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?
Feb 16	awarded	● Notable Question
Feb 15	revised	excision in algebraic de Rham cohomology added 1 characters in body; added 2 characters in body
Feb 15	comment	Using schemes to prove things about rings Why do you apologize for asking a big list question?
Feb 15	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.
Feb 14	awarded	● Popular Question
Feb 8	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 :)
Feb 8	revised	Why is Set, and not Rel, so ubiquitous in mathematics? deleted 4 characters in body
Feb 8	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 $\alpha \in \mathsf{Ord}$.
Feb 8	awarded	● Good Question
Feb 7	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.
Feb 7	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?
Feb 7	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.
Feb 7	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 $\mathsf{Rel}^\Delta$?
Feb 7	comment	Why is Set, and not Rel, so ubiquitous in mathematics? Thanks for editing the title.
Feb 7	awarded	● Nice Question
Feb 7	asked	Why is Set, and not Rel, so ubiquitous in mathematics?
Feb 6	comment	Ring with three binary operations @NoahStein: appearently, one cannot have too much "distributivity": see my answer about Eckmann-Hilton theorem.

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