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seen Sep 14 at 4:04

Oct
10
awarded  Nice Question
Sep
30
awarded  Explainer
Sep
11
comment Is every local ring a valuation ring?
But, $F$ isn't the field of fractions of $\{0,1\}\subseteq F$?
Sep
11
revised Is every local ring a valuation ring?
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Sep
11
revised Difference between two concepts of homotopy for simplicial maps?
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Sep
11
comment Difference between two concepts of homotopy for simplicial maps?
@ZhenLin It seems that you are right, if the definition of the product is essentially same as the one in Goerss & Jardine. It might be a mistranlation from Russian.
Sep
11
comment Difference between two concepts of homotopy for simplicial maps?
@QiaochuYuan Simply homotopy of $f,g\colon X\to Y$ here, informally speaking, is just a simplicial map $F\colon\Delta[1]\times X\to Y$ from a cylinder $\Delta[1]\times X$ (triangulated canonically, where $\Delta[1]$ is just the simplicial set associated with $I=[0,1]$, i.e., $1$-simplex) to $Y$, both of which are simplicial sets. Sorry for my ignorance. I don't know what you're referring to. Thanks, anyway.
Sep
11
revised Difference between two concepts of homotopy for simplicial maps?
added 126 characters in body
Sep
11
revised Finite intersection property in any metric space
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Sep
11
asked Difference between two concepts of homotopy for simplicial maps?
Aug
31
revised Differentiable manifolds $\mathscr C^k$ vs. $\mathscr C^\infty$
edited body
Aug
27
comment 6.17 Theorem : Show that $f \ \ \in \mathfrak R(\alpha)$ if and only if $ f\alpha' \ \ \in \mathfrak R$ ( walter rudin)
It follows from Rudin's argument that the upper and lower (Darboux) integrals of $fd\alpha$ and $f\alpha'dx$ are the same.
Aug
27
comment Differential identity and wedge products
$f\omega$ is just $f\wedge\omega$ where $f$ is considered as a $0$-form, and $d(\omega_1\wedge\omega_2)=d\omega_1\wedge\omega_2+(-1)^p\omega_1\wedge d\omega_2$ where $\omega_1$ is a $p$-form.
Aug
27
comment $f\in C(\mathbb{R})$. What does it mean?
But it's usually denoted as $C^n(\mathbb R)$ or $\mathcal C^n(\mathbb R)$ as well as $\mathcal C^0(\mathbb R)$ without parentheses.
Aug
27
comment A question on short exact sequences.
I found learning diagram chasing isn't that easy for a beginner from books, but there're two materials which seems more accessible: Hatcher's Algebraic Topology, pp115, subsection Relative Homology Group, and Eisenbud's Commmutative Algebra, pp637, subsection A3.7.
Aug
27
answered Prove $a^3+b^3+c^3\ge a^2+b^2+c^2$ if $ab+bc+ca\le 3abc$
Aug
27
revised How to graph functions without a calculator?
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Aug
26
comment Differentiability of non-analytic complex functions
Well, and by Looman-Menchoff theorem, a continuous complex function is holomorphic in some region if and only if it satisfies Cauchy-Riemann equations everywhere.
Aug
25
accepted Homology of a finite graph follows from Mayer-Vietoris sequence?
Aug
24
comment Homology of a finite graph follows from Mayer-Vietoris sequence?
@LeeMosher Thanks. I've edited to include these.