Question

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

Answer 1

A′=(b,c,e)
A′=(b,d,e)
A′=(b,e)
A′=X

Answer 2

@zzr0ck3r

Answer 3

i think option B

Answer 4

@zzr0ck3r

Answer 5

am i correct ?

Answer 6

Do you mean interval [ ] ?

Answer 7

or { }

Answer 8

do you mean the empty set \(\emptyset\) and not that weird thing?

Answer 9

i think {} and that weird thing is empty set

Answer 10

ok can you edit it to make sense?

Answer 11

these things mean different things...

Answer 12

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

Answer 13

@zzr0ck3r

Answer 14

why do you think B?

Answer 15

because that is A complement with X

Answer 16

So you think that the set of limit points is defined to be the compliment?

Answer 17

please i will be happy if you explain the concept with you

Answer 18

I already have.

Answer 19

What is a limit point?

Answer 20

it is the boundary points or closed interval points

Answer 21

@zzr0ck3r

Answer 22

So you did not read a thing I wrote on the last problem?

Answer 23

Go back and read that and then tell me what a limit point is

Answer 24

a point for which every neighborhood contains at least one point belonging to a given set.

Answer 25

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.

Answer 26

ok, so what are the open sets containing b?

Answer 27

,{b,c,d,e}

Answer 28

does that intersect A? in other words, does that share any points with A?

Answer 29

yes c

Answer 30

ok, what are the open sets containing d?

Answer 31

{c,d},{a,c,d},{b,c,d,e}

Answer 32

I shuold be saying intersect A at some other point...

Answer 33

ok do all of those sets intersect A at some other point other than d?

Answer 34

why are you using caps?

Answer 35

d is not in A... try again

Answer 36

sorry . 'a' for the first and 'c' for the second and third

Answer 37

right

Answer 38

ok and with e we get the same thing as with b right?

Answer 39

yes

Answer 40

So your option is looking good, but maybe some other point is also a limit point.

What open sets contain a?

Answer 41

Better yet, do all of the open sets that contain a also intersect A at some point other than a?

Answer 42

{a},{a,c,d}

Answer 43

do all of the open sets that contain a also intersect A at some point other than a?

Answer 44

yes

Answer 45

but not {a}

Answer 46

right so you mean no then?

Answer 47

yes

Answer 48

then a is not a limit point

what about c?

Answer 49

is c a limit point?

Answer 50

yes ,{a,c,d} because it intersects A

Answer 51

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

Answer 52

,{c,d},{a,c,d},{b,c,d,e} contain c

Answer 53

do all of those intersect A at some point different than c?

Answer 54

only {a,c,d}

Answer 55

so there is at least one that does not?

Answer 56

then c is NOT a limit point.

So yes your option B is the answer, but not for the reason you listed :)

Answer 57

ok. thanks . i have to view this page more often to understand this

Answer 58

Let
A=(0,1]⋃2
be a subset of
R

Answer 59

what are the limit points

Answer 60

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.

Answer 61

ok thanks

Answer 62

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 \(x\).

Answer 63

i think 0 and 1

Answer 64

ok

Answer 65

you think what 0 and 1?

Answer 66

Let
A=(0,1]⋃2
be a subset of
R

Answer 67

done