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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?
Sep
11
comment What tools would I use to answer the following topology question?
Thank you. And which part in the linked document is relevant to the question? It seems to me that the document only deals with finite dimensional products but humour me and point me to the relevant theorem in the document.
Sep
11
comment What tools would I use to answer the following topology question?
So: compact implies sequentially compact implies every sequence has a convergent subsequence.
Sep
11
comment What tools would I use to answer the following topology question?
Can you state the Bolzano Weierstrass property?
Sep
11
comment What tools would I use to answer the following topology question?
What is N? The natural numbers or a natural number?
Sep
10
comment Arbitrary Intersection of Bounded Sets Is Bounded
@Josué Exactly. I was just about to post an answer but now that you figured it out yourself I will not.
Sep
10
comment Proving with completeness axiom
@MarianoSuárez-Alvarez I assumed he meant if $a \in E$ then $a \le 0$.
Sep
1
comment Analysis in $R^n$
@user262860 Yes, it is false.