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

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In summary, a closed set in R^2 is a collection of points in a two-dimensional space that includes all its boundary points. It can be visualized as a "closed off" shape with no gaps or missing points. Examples include squares and circles. Understanding closed sets in R^2 is important in various mathematical fields and has practical applications. To determine if a set in R^2 is closed, one can check if its complement is open. The main difference between a closed set and an open set in R^2 is that a closed set includes all its boundary points, while an open set does not.
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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?
 

What is a closed set in R^2?

A closed set in R^2 is a collection of points in a two-dimensional space that includes all its boundary points. This means that the set is "closed off" and does not have any missing points or gaps.

What is an example of a closed set in R^2?

An example of a closed set in R^2 could be a square with all its edges and corners included. Another example could be a circle with its entire circumference included.

Why is it important to understand closed sets in R^2?

Understanding closed sets in R^2 is important in various areas of mathematics, such as topology and geometry. It also has practical applications in fields such as engineering and physics.

How can I determine if a set in R^2 is closed?

A set in R^2 is closed if it contains all its boundary points. This can be determined by checking if the set's complement (the points not included in the set) is open. If the complement is open, then the set is closed.

What is the difference between a closed set and an open set in R^2?

A closed set includes all its boundary points, while an open set does not. This means that an open set can have gaps or missing points, while a closed set does not.

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