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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?