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anonymous
 one year ago
With the standard topology on R,which one of the sets is open in R?
anonymous
 one year ago
With the standard topology on R,which one of the sets is open in R?

This Question is Closed

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

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i fink this is the answer but i have other options

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.1so why is this open? Can you write it in interval notation?

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.1but the absolute value sign means you also get (1,1/2). Do you see that? 1/2 < 0.8<1

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.1So the set, in interval notation, is \[(1, \dfrac{1}{2})\cup (\dfrac{1}{2}, 1)\]

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.1I was just showing you that you get negative number in there as well

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

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok. now i got it. because of the absolute value .

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0should i post the other options?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[{x: \frac{1}{2} < x\leqslant1} \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0now this is neither open or close in R . right ?

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.1Can you write it in interval notation?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0please don't shout on me. i will try

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i mean please do not get angry if i fail

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.1I don't even know how to respond to that.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what if i say it can not be written as union of open sets

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.1almost, the 1 gets a [ also

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.1\([1, 0.4)\cup(0.5,1]\)

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.1ok what is a closed set?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0a close set is a close interval. meaning that every set that has it boundary involve is close . because if we take a small radius around any boundary, it will not be in the set

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0no. i am here,network is getting bad

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.1Ok, closed intervals are closed sets, but that is not all of them. R is both open and closed, and so is the empty set, and neither of those are closed intervals. A set is closed if its compliment is open. Do you know what a compliment is?

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.1Ok, we can go with boundary, does this set contain all of its boundary points? If not, which 2 does it not contain?

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.1Aight man, I am sorry about the internet, but this is taking way to long. It took about 35 minutes to get replies. I will be back tomorrow.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0am sorry sir. my network is really poor

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0it does not contain all its boundary point. it contains only one which is 1 but does not contain 1/2. so it is half open and half close

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.1Its boundary points are 1, 1/2, 1/2, and 1. While it is not a great idea to think of every open/closed set as an interval, loosely said, the boundary points are the endpoints of any broken up union of sets.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so, x:1/2<x⩽1 is neither open nor close . so is it right to say that the only open sets in R in the options given above are \[x:1/2<x<1 \] and the close set in the option above in R is \[x:1/2\lex⩽1 \] right?

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.1yes, unless I did not see all the options

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0let me close this question and ask another . can i?
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