Example of Closed Set in R^2: Help Needed!

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An example of a closed set S in R^2 where the closure of its interior is not equal to S is the set of finite points, such as S = { (0,0), (1,1), (2,2) }. The interior of this set is empty, leading to the closure of the interior also being empty, which is not equal to S. This highlights the distinction between closed sets and their interiors in topological spaces.

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pantin
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help! 'set' question

Give an example in the set notation of a CLOSED set S in R^2 such that the closure of int S is not equal to S.

I originally used the set

s={ (x,y) : 0 <x^2+y^2<1}
but I just noticed it's not closed set!
...

can anyone give me an example?

Thanks!
 
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No, but I can suggest something to try: if S is a finite set of points, what is its interior? What is the closure of that?
 

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