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anonymous
 one year ago
pleas can anyone helm me prove that arbitrary intersection of open set is not open????
anonymous
 one year ago
pleas can anyone helm me prove that arbitrary intersection of open set is not open????

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jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.0Are you working with topological spaces or metric spaces in this assignment? Basically, what is the definition of open set that you are to use?

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.0OK. Thanks, that helps us know what to focus on.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.0After consulting my textbook, it seems that all you need is a counterexample to prove this.

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0Let A, B are open set then \(A\cup B\) is an open set also Suppose \(A\cap B \) is not empty consider compliment of \(A\cap B\) that is the set of element in A or in B and we know that that set is open, hence \(A\cap B\) is closed.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok sir but what textbook do you thick should be the best to study metic space for a dummie like me ?

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.0I like that @Loser66. Very elegant.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@Loser66 can you be specific using the real line R here sir , please

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0hey @jtvatsim now is your turn :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0because i get more confuse trying to understand my text book.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.0But sometimes the intersection of two open sets IS open. :) Consider (0,3) and (1,2). The intersection is (1,2) which is still open. It is arbitrary intersections that cause problems.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.0Anyways, to answer your question @GIL.ojei I have yet to find a good introduction to metric spaces. I've struggled with almost all textbooks on the subject. But, I did find this example for the real line.

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0I think that the arbitrary union of open sets is open

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.0Consider the set of open intervals centered around the point 0. That is, the family (1/i, 1/i). Then, consider the infinite intersection \[\cap_{i = 1}^\infty (1/i, 1/i)\] You will see that as this proceeds to infinity the intervals converge to (0,0) or just the single point {0}. Since a single point is not open, we have shown that an arbitrary intersection of open intervals need not be open.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0here is a link @Michele_Laino ,@jtvatsim and @Loser66 ,,, please hepl explain page 17 and 18(remark 1 and 2)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0http://nou.edu.ng/uploads/NOUN_OCL/pdf/edited_pdf3/MTH%20301.pdf

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0Go to this page , read section 2.1. It is wayyyyyyyyyyy clearer than your text book https://books.google.com/books?id=mMBY5jdjGfoC&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0according to the observation of @jtvatsim if the result of an arbitrary intersection, for example an infinite intersection, is a one point set, then we can show that in a metric space, which is also a topological space, any one point set is a closed set

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@Loser66 can't find a way to read the text book

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0oh, you are not in America. That's why you can't open that site. Am I right?

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0How about this? watch section 14 topology. https://www.youtube.com/watch?v=FHL4udeLf9Q&index=14&list=PLZzHxk_TPOStgPtqRZ6KzmkUQBQ8TSWVX

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.0This one is different than Loser66's but I've heard good things about this one: http://www.topologywithouttears.net/topbook.pdf

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok hard that before but he did not explain matric space in dept

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0metric space is a set equipped with a function, called distance

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok thanks @Michele_Laino

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thanks @Loser66 and thats @jtvatsim .. you guys have been helpful
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