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Sep
14
comment About the proof of the existence of a decomposition of subset of $\mathbb{A}^n$
@Zhen, thank you for your help. I cannot understand the last part of your proof showing that any maximal irreducible subset is closed. What does the expression $U \cap Y \subset Z \cap Y$ mean ?
Sep
13
comment About the proof of the existence of a decomposition of subset of $\mathbb{A}^n$
Thank you for answering my question. Could you explain the last line of your answer ? "Note that the only property of Y we need is it has finitely many irreducible components."
Sep
12
asked About the proof of the existence of a decomposition of subset of $\mathbb{A}^n$
Jul
24
accepted Is it true that if $\alpha \in \operatorname{Frac}(A)$ and $s\alpha \in A$, then $\alpha \in S^{-1}A$?
Jul
24
comment Is it true that if $\alpha \in \operatorname{Frac}(A)$ and $s\alpha \in A$, then $\alpha \in S^{-1}A$?
I think I get it thanks to your additional comment "we don't care what the original form of $\alpha$ is/was".
Jul
24
comment Is it true that if $\alpha \in \operatorname{Frac}(A)$ and $s\alpha \in A$, then $\alpha \in S^{-1}A$?
Thank you, @GeorgesElencwajg. Now, I see that my assumption was wrong.
Jul
24
comment Is it true that if $\alpha \in \operatorname{Frac}(A)$ and $s\alpha \in A$, then $\alpha \in S^{-1}A$?
It is the revised third edition.
Jul
24
asked Is it true that if $\alpha \in \operatorname{Frac}(A)$ and $s\alpha \in A$, then $\alpha \in S^{-1}A$?
Jan
27
accepted Containment of extension fields in a Bourbaki proof: $K(S)\subset K(B)$?
Jan
27
asked Containment of extension fields in a Bourbaki proof: $K(S)\subset K(B)$?
Jan
15
comment Why is it biholomorphic?
Thank you for your detailed explanation. Then, I made a mistake in using the chart $(U_1,z)$ to evaluate the function $\phi_2$. And, each chart $\psi:U \rightarrow V$ on any Riemann surface is biholomorphic since $\psi \circ \psi^{-1} = \mbox{id}_V$ is biholomorphic. Am I right ?
Jan
13
comment Why is it biholomorphic?
I thought that $\phi_2'(\infty)\neq 0$ is a necessary condition for the existense of the holomorphic inverse mapping of$\phi_2$ at $\infty$.
Jan
13
asked Why is it biholomorphic?
Dec
23
comment Why is it trivial for compact Riemann surfaces to have a countable topology?
Thank you ! Now it is clear for me too.
Dec
23
comment Why is it trivial for compact Riemann surfaces to have a countable topology?
Thank you @ChrisEagle and ZevChonoles for quick answers. The above is the direct quotation from the book. I understand it as second countable or "has a countable base for its topology" as you suspect.
Dec
23
asked Why is it trivial for compact Riemann surfaces to have a countable topology?
Oct
19
accepted Why does the continuity of $(x,y) \rightarrow x-y$ mean the commutativity of a topological group?
Oct
19
awarded  Scholar
Oct
19
accepted Is it always true that |1+1|>1 in an Archimedean valuated field?
Oct
19
awarded  Supporter