- #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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