anonymous
  • anonymous
Let X=(a,b,c,d,e)andτ=(X,ϕ,[a],[c,d],[a,c,d],[b,c,d,e]).LetA=[a,c] , then set A′of limit points of A is given by
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
A′=(b,c,e) A′=(b,d,e) A′=(b,e) A′=X
anonymous
  • anonymous
anonymous
  • anonymous
i think option B

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anonymous
  • anonymous
anonymous
  • anonymous
am i correct ?
zzr0ck3r
  • zzr0ck3r
Do you mean interval [ ] ?
zzr0ck3r
  • zzr0ck3r
or { }
zzr0ck3r
  • zzr0ck3r
do you mean the empty set \(\emptyset\) and not that weird thing?
anonymous
  • anonymous
i think {} and that weird thing is empty set
zzr0ck3r
  • zzr0ck3r
ok can you edit it to make sense?
zzr0ck3r
  • zzr0ck3r
these things mean different things...
anonymous
  • anonymous
X=(a,b,c,d,e)andτ=(X,ϕ,{a},{c,d},{a,c,d},{b,c,d,e}).LetA={a,c} , then set A′ of limit points of A is given by
anonymous
  • anonymous
zzr0ck3r
  • zzr0ck3r
why do you think B?
anonymous
  • anonymous
because that is A complement with X
zzr0ck3r
  • zzr0ck3r
So you think that the set of limit points is defined to be the compliment?
anonymous
  • anonymous
please i will be happy if you explain the concept with you
zzr0ck3r
  • zzr0ck3r
I already have.
zzr0ck3r
  • zzr0ck3r
What is a limit point?
anonymous
  • anonymous
it is the boundary points or closed interval points
anonymous
  • anonymous
zzr0ck3r
  • zzr0ck3r
So you did not read a thing I wrote on the last problem?
zzr0ck3r
  • zzr0ck3r
Go back and read that and then tell me what a limit point is
anonymous
  • anonymous
a point for which every neighborhood contains at least one point belonging to a given set.
zzr0ck3r
  • zzr0ck3r
Also, when you reply to something I have commented on, I get tagged and see it. There is no reason to tag me more than once on a post.
zzr0ck3r
  • zzr0ck3r
ok, so what are the open sets containing b?
anonymous
  • anonymous
,{b,c,d,e}
zzr0ck3r
  • zzr0ck3r
does that intersect A? in other words, does that share any points with A?
anonymous
  • anonymous
yes c
zzr0ck3r
  • zzr0ck3r
ok, what are the open sets containing d?
anonymous
  • anonymous
{c,d},{a,c,d},{b,c,d,e}
zzr0ck3r
  • zzr0ck3r
I shuold be saying intersect A at some other point...
zzr0ck3r
  • zzr0ck3r
ok do all of those sets intersect A at some other point other than d?
zzr0ck3r
  • zzr0ck3r
why are you using caps?
zzr0ck3r
  • zzr0ck3r
d is not in A... try again
anonymous
  • anonymous
sorry . 'a' for the first and 'c' for the second and third
zzr0ck3r
  • zzr0ck3r
right
zzr0ck3r
  • zzr0ck3r
ok and with e we get the same thing as with b right?
anonymous
  • anonymous
yes
zzr0ck3r
  • zzr0ck3r
So your option is looking good, but maybe some other point is also a limit point. What open sets contain a?
zzr0ck3r
  • zzr0ck3r
Better yet, do all of the open sets that contain a also intersect A at some point other than a?
anonymous
  • anonymous
{a},{a,c,d}
zzr0ck3r
  • zzr0ck3r
do all of the open sets that contain a also intersect A at some point other than a?
anonymous
  • anonymous
yes
anonymous
  • anonymous
but not {a}
zzr0ck3r
  • zzr0ck3r
right so you mean no then?
anonymous
  • anonymous
yes
zzr0ck3r
  • zzr0ck3r
then a is not a limit point what about c?
zzr0ck3r
  • zzr0ck3r
is c a limit point?
anonymous
  • anonymous
yes ,{a,c,d} because it intersects A
zzr0ck3r
  • zzr0ck3r
is that the only open set that contains c? Remember, we only have to find one that does not intersect at some point other than c
anonymous
  • anonymous
,{c,d},{a,c,d},{b,c,d,e} contain c
zzr0ck3r
  • zzr0ck3r
do all of those intersect A at some point different than c?
anonymous
  • anonymous
only {a,c,d}
zzr0ck3r
  • zzr0ck3r
so there is at least one that does not?
zzr0ck3r
  • zzr0ck3r
then c is NOT a limit point. So yes your option B is the answer, but not for the reason you listed :)
anonymous
  • anonymous
ok. thanks . i have to view this page more often to understand this
anonymous
  • anonymous
Let A=(0,1]⋃2 be a subset of R
anonymous
  • anonymous
what are the limit points
zzr0ck3r
  • zzr0ck3r
remember to show something is not a limit points you need to show that it has an open set around it that intersects the set at some point OTHER than the point in question. I did not stress that in the last post.
anonymous
  • anonymous
ok thanks
zzr0ck3r
  • zzr0ck3r
For a subset \(A\subset X\) a limit point \(x\) of \(A\) is a point in \(X\) (not necessarily in \(A\)) such that all open sets containing it intersect \(A\) at some point other than \(x\).
anonymous
  • anonymous
i think 0 and 1
anonymous
  • anonymous
ok
zzr0ck3r
  • zzr0ck3r
you think what 0 and 1?
anonymous
  • anonymous
Let A=(0,1]⋃2 be a subset of R
zzr0ck3r
  • zzr0ck3r
done

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