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 Jul25 comment Good problem book on Abstract Algebra I admit they are really good. Still, I believe it is better to look around just to see what problems do other people see around. I am not a math major and my college/university does not have these courses, so I am really scarce on exposure. Jul25 comment Good problem book on Abstract Algebra Hi, thanks for your comments. Herstein does have a fresh perspective of problems and exposition. I read it and already like how he presented the three different proofs of Sylow Theorems including the very basic combinatorial one. Thanks Jul25 comment Continuous mappings pull back closed sets to closed sets I was not taught that way, not using that or equivalent definition, I was taught as I wrote in that comment. While, I did learn the new definition, once in a while the old habit unconsciously takes over. I hope, I get used to the new one fast enough though :-) Jul24 comment Continuous mappings pull back closed sets to closed sets Okay, then it is trivial. You just take the complements and get done. Somehow, now, the question is something else, while the actual difficulty was something else. I guess, I would edit the question and someone can edit his answer and then, I would accept it so that it represents what actually happened? Jul24 comment Continuous mappings pull back closed sets to closed sets I am very sorry, I meant to use $G'$, will correct it if possible. Jul24 comment Continuous mappings pull back closed sets to closed sets I guess, I am not using the definition of $f^{-1}\left(G\right)$ properly. I am using the definition that $f^{-1}\left(G\right)$ exists only when $f$ is onto and if it is not then $f^{-1}\left(G\right)$ is a loose term for $f^{-1}\left(H\right)$ where $H$ is the range. If someone one can make it more clear to me, it would be better. Jul24 comment Continuous mappings pull back closed sets to closed sets So lets say, $Z \in Y$ is the "range" of $f$ so that $f:X \rightarrow Z$ is an onto mapping. Then, if $G$ is closed in $Y$, then $G^{-1}$ is open in $Y$, but we are now considering $H = G^{-1} \bigcap Z$, how do I know that is also open? As far as I know, $H$ is open as a subset of $Z$ (which should be a subspace of $X$) in and only if it is the intersection with $Z$ of an open set which it is, but what about $H$ in $X$? Jul24 comment Continuous mappings pull back closed sets to closed sets Definition of closed is that the a contains all its limit points where $a$ is a limit point of $X$ if for every open sphere $S_{\epsilon}\left(a\right)$ there exists an $x \in X$ such that $x \in S_{\epsilon}\left(a\right)$ Jul24 comment Continuous mappings pull back closed sets to closed sets Your second step would be true only for onto mappings, while the textbook says $f$ is an into mapping, or am I missing something? Jul24 comment Continuous mappings pull back closed sets to closed sets But the mapping is an into mapping, how do I know $f^{-1}$ exists for all Y Jan17 comment Difficulties with Chapter 2 in Rudin @Adam: I tried to have a go ;-). Was not very comfortable. Will try again after reading some more. Jan12 comment Difficulties with Chapter 2 in Rudin thanks... expecially for the problems, though I will need some time. But I'll get back to you as soon as I can. Jan12 comment Difficulties with Chapter 2 in Rudin "Because the subject is relatively standard, other texts may provide a different perspective on a topic that provides you with that "ah-ha" moment -- why have one teacher when you can have many? " Yeah, though so, but I was afraid, (see my comment on answer by Samuel Reid about multivariable calculus book.) Hence, I was kind of reluctant. But, I will try now, I have Royden with me. I will get korner if possible and see. Jan12 comment Difficulties with Chapter 2 in Rudin thanks for the clarification, was just browsing through one of the multivariate calculus book, they said the same thing about compactness as described by Samuel Reid, so I had an idea, but kahen's explanation clarifies it. Thank You! Anyway, that is cleared now. But, boy, was I confused when I read that book!! Jan12 comment Difficulties with Chapter 2 in Rudin +1 : Thanks. I am an electrical engineer too. I was good in mathematics in school and have a decently good olympiad experience, and so thought that I may be able to handle Rudin well ;-). I will take your advice of keeping other books as supplement. Thanks for your advice. Jan12 comment Difficulties with Chapter 2 in Rudin Thanks for the answer. And you are right, I am also having problems with the limit point. I found your question some time before, but I guess I did not read it well enough. I will go back to it and read it again more carefully. And thank you for the hints. I wil try to follow your suggestions. :-) And of course the encouragement. :-) Jan12 comment Difficulties with Chapter 2 in Rudin @AmiteshDatta: Thanks for the guideline. It will help. Jan12 comment Difficulties with Chapter 2 in Rudin @t.b. No, I am using Principles of Mathematical Analysis. Jan12 comment Difficulties with Chapter 2 in Rudin @ncmathsadist Yes I have been working out the problems. Dec4 comment Cardinality of set containing true order relations from a power set :)... No problems.. You took out time to edit it.. That's enough! :)