Rudy the Reindeer
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 Sep 28 comment Showing that an inclusion is null homotopic @morphic I don't remember. Sep 28 comment finding a linear transformation I might be missing something but is there any reason why you can't just define $\theta = \alpha \oplus \beta$? Sep 22 comment Reference for guided exercises in Group Theory Have a look at Joseph Gallian's Contemporary Abstract Algebra. It contains solutions to all odd numbered problems. Sep 19 comment $f,g,h$ be a holomorphic functions such that $|f(z)|+|g(z)|+|h(z)|=1$ @Potato Ok, right, of course it's enough to show they are constant on an open subset. I believe you but I don't yet see how to get the open subset. Concretely, if they are not constant each one has some open subset on which they are non zero, say $U_f, U_g$ and $U_h$. How do we guarantee that their intersection is non empty? Sep 19 comment $f,g,h$ be a holomorphic functions such that $|f(z)|+|g(z)|+|h(z)|=1$ So $g$ is the square root of $f$ but if $f$ is zero anywhere the square root is not differentiable in which case $g$ would not be holomorphic. So your answer assumes that $f,g,h$ are non-zero on $U$. Or am I missing something here? Sep 18 comment Functions of a Complex Variable and Complex Differentiability Did you mean $f'(z)\neq0$? Sep 18 comment Suppose that $f: D \to D$ is analytic with $f(0) = 0$. Show $f$ assumes all values $z$ with $|z| \leq 1/2$ with given assumption $D$ is most probably the open unit disk in the complex plane. Sep 18 comment Complex Differentiability with respect to x and y @user251257 Got it. Thank you for your comments! I will edit the answer. Sep 18 comment Complex Differentiability with respect to x and y @user251257 Good point. Let me find the mistake. Sep 16 comment What tools would I use to answer the following topology question? @user254665 I see. Thank you for the comment. Sep 13 comment polynomial rings in two variables I don't understand how you apply the UP. Could you elaborate please? Sorry for being slow. Sep 13 comment polynomial rings in two variables The inclusion composed with the projection? Sep 13 comment polynomial rings in two variables What is the unique mapping that you mention in your first sentence? Sep 12 comment Functions from $\mathbb{R}^{n}$ to $[0,1]$. Nice answer and thank you for your comment! Sep 12 comment Find closure of $G=\bigcup_{x\neq0}G_x$ $x\in \mathbb R$? Or what? Sep 12 comment Uniform convergence of a sequences of functions to a complete metric space @Andrew I tried to answer your edit but I don't understand the second question in the edit so I will answer the first for now. Sep 11 comment Is the following set closed in $\ell_{p}$ for $1\le p$? What a nice answer! Sep 11 comment What tools would I use to answer the following topology question? @user254665 Thank you for your comment. I looked at the document linked to in the other answer but could not find Bolzano Weierstrass for cardinalities greater than finite. Where can I find it for countably infinite? Sep 11 comment An example to show that this set of continuous function is not closed. An example of a norm? Or what? Sep 11 comment What tools would I use to answer the following topology question? @CameronWilliams I had never heard of Bolzano Weierstrass property before and then I skimmed the linked document in absalon's answer but it seems it's only about finite dimensional products. Do you know where I can find the BW property stated for infinite products?