Limit points and exterio points Quick quesiton

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SUMMARY

The assertion that X\lim(A) = ext(A) for a subset A of a metric space X is confirmed as true. The discussion centers on the definitions of limit points (lim(A)) and exterior points (ext(A)), with a focus on proving that lim(A) is closed. The example of A as a one-point set is utilized to illustrate the concepts, emphasizing the distinction between limit points and isolated points.

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  • Understanding of metric spaces
  • Familiarity with limit points and exterior points in topology
  • Knowledge of closed sets in a metric space
  • Basic proof techniques in mathematical analysis
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  • Study the properties of limit points in metric spaces
  • Explore the concept of closed sets and their characteristics
  • Investigate the relationship between isolated points and limit points
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Mathematicians, students of topology, and anyone interested in understanding the properties of limit and exterior points in metric spaces.

Buri
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Is the following true?

X\lim(A) = ext(A), where A is a subset of a metric space X.

I think I've found a proof, but I don't feel very secure about it. So could someone just tell me if this is a correct assertion? What I'm trying to prove is that lim(A) is closed.

Thanks
 
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Take A being a one-point set. What is lim(A)? What is ext(A)?
 
I hate isolated points! lol Thanks
 

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