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anonymous
 one year ago
Let R be endowed with the usual standard topology. Consider Y = [1,1] as a subspace of R. Which one of the following sets is closed in Y?
anonymous
 one year ago
Let R be endowed with the usual standard topology. Consider Y = [1,1] as a subspace of R. Which one of the following sets is closed in Y?

This Question is Closed

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0{x: \frac{1}{2}\ < x < 1}

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.2First, let us talk about what an open set will look like.

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.2An open set in the subspace, will be of the form \(A\cap [1,1]\) where \(A\) is open in \(\mathbb{R}\).

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.2Every open set in \(\mathbb{R}\) can be written as the union of intervals of the form \((a, b)\).

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.2Can this be written in the form \(A\cap [1,1]\) where \(A\) is open in \(\mathbb{R}\)? If so, show me. If not, why not?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0please wait let me think

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes , it can be written like that

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[(1,1/2) \cup(1/2,1)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so that the union =(1,1)

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.2I think you mean the following: Consider \((1, 1/2)\cup (1/2, 1)\). Since \((1, 1/2)\cup (1/2, 1)\) is open in \(\mathbb{R}\) we have that \([1,1]\cap[(1, 1/2)\cup (1/2, 1)]\) is open in the subspace \([1,1]\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes but please explain this \[[−1,1]∩[(−1,−1/2)∪(1/2/1)] \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i know that [−1,1]∩[(−1,−1/2)∪(1/2,1)] is open in R

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0but i know that [1,1] is close in R.

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.2and in the subspace. because it can be written in the form of [1,1] intersected with an open set in R

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.2This one is sort of trivial, because it is a subset of [1,1] so it equals the intersection of itself and [1,1]. Since it was open in R to begin with, it is open in the subspace.

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.2I really think if you ask about one of the other options, this one will make more sense...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok but do you have any examples to make me understand more?

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.2Didn't they give you more options? like I think \[\{x\mid \frac{1}{2}\le x < 1\}\] Was this not an option?

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.2and \(\{x\mid \frac{1}{2}< x \le 1\}\) and \(\{x\mid \frac{1}{2}\le x \le 1\}\)

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.2You here man? These are yes or no questions :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0NETWORK IS TOOOOOO POOR

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0OK, NOW it means that the option that is close is \[{{x∣1/2≤x≤1} } \] is the close set. ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0now, with same options, which of them are open in the standard topology on R and which of them are close?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0my guess is that [1/2, 1] is close in R and (1/2,1} is open in R. am i right ? what then will [1/2, 1) and (1/2,1] be . open or close ? please explain

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.2Are you asked if they are open, or closed. A set can be neither open nor closed. A set can be both open and closed.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0which of the options are open in r and which are close in R and which are nither open or close and which are both open and close in the options above ?

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.2It does not help you at all for me just to tell you. You need to go with the definition and figure it out. Then it will always make sense.

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.2Which one would you like to look at?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[{x∣1/2<x≤1} \] this one first, is it open or close in R . i guess it is neither

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.2Try and write that set as the union of open intervals.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0will it be \[(1,\frac{ 1 }{ 2})\cup(\frac{ 1 }{ 2 },1]\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0which book or site can i lean how to do this sir?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i thick it can not be written

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.2\([1,\frac{ 1 }{ 2})\cup(\frac{ 1 }{ 2 },1]\)

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.2The book I gave you covers this in detail.

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.2Answer this please \([(2,\dfrac{1}{2})\cup(\dfrac{1}{2},2)]\cap[1,1]= \ ?\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i have only learnt open sets, close sets, neither open or close , . but i saw an example like that but it only stated the open and the close sets

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.2Just answer the last question I asked

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the answer to that question you asked is (1,1)

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.2not at all. You really need to go spend some time learning basic set theory, else there is no way you will learn this. How do we know a set is open in a subspace topology?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i have not studied sub base sir

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.2I have said about 5 times the answer to that question. This lets me know that you are not really studying anything I say.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0at first i thought the answer to that your question is empty set but i was not sure

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.2You are just guessing and repeating things.... you are not learning The fact that you cant write \(\{x\mid \frac{1}{2}<x\le 1\}\) in interval notation tells me that you are very far from being ready for this.

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.2I am not trying to be rude, but it is a waste of time.

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.2It took me months to learn what you are trying to brush over in 20 mins, it will not work, you will not pass the test with this method. I gave you a book, and it has problems in it. You should read the book and do the problems, that is the ONLY way to learn math. You may ask me any question you want, but I tell you now that you are wasting your time.

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.2If you want to keep on with this question, then scroll up and find out where I answerd the following question: How do we know a set is open in a subspace topology? Find the answer and explain what I said. Then we will continue

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i will do that. let me try to learn that, only that i am confuse because the first question was on [1,1] but now it said which of the options is open in R

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.2we are talking about the first question.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ohh. i thought we have answered the first question

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.2Ok Close this and ask the new question :)
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