- #1
splash_lover
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Suppose that S=[0,1)U(1,2)
a) What is the set of interior points of S?
I thought it was (0,2)
b) Given that U is the set of interior points of S, evaluate U closure.
I thought that U closure=[0,2]
c) Give an example of a set S of real numbers such that if U is the set of interior points of S, then U closure DOES NOT equal S closure
This one I was not sure about, but here is my example:
S=(0,3)U(5,6) S closure=[0,3]U[5,6]
U=(0,6) U closure=[0,6]
d) Give an example of a subset S of the interval [0,1] such that S closure=[0,1].
I said if the subset S=(0,1/2)U(1/2,1) then S closure=[0,1]
Are my answers right for these? If not could you please explain what the answer is in detail?
a) What is the set of interior points of S?
I thought it was (0,2)
b) Given that U is the set of interior points of S, evaluate U closure.
I thought that U closure=[0,2]
c) Give an example of a set S of real numbers such that if U is the set of interior points of S, then U closure DOES NOT equal S closure
This one I was not sure about, but here is my example:
S=(0,3)U(5,6) S closure=[0,3]U[5,6]
U=(0,6) U closure=[0,6]
d) Give an example of a subset S of the interval [0,1] such that S closure=[0,1].
I said if the subset S=(0,1/2)U(1/2,1) then S closure=[0,1]
Are my answers right for these? If not could you please explain what the answer is in detail?
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