Finite intersection of closed sets is not necessarily closed

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SUMMARY

The discussion centers around a misunderstanding of a statement in Rudin's "Analysis" regarding the intersection of closed sets. It clarifies that while an arbitrary intersection of closed sets is always closed, the finite intersection of closed sets is indeed closed. The confusion arose from a misreading of the text on page 34, which led to a request for examples that do not exist, as the original claim was incorrect.

PREREQUISITES
  • Understanding of basic topology concepts
  • Familiarity with closed sets in mathematical analysis
  • Knowledge of Rudin's "Analysis" textbook
  • Ability to interpret mathematical literature
NEXT STEPS
  • Review the properties of closed sets in topology
  • Study examples of arbitrary intersections of closed sets
  • Read further sections of Rudin's "Analysis" for deeper insights
  • Explore counterexamples in topology to solidify understanding
USEFUL FOR

Students of mathematics, particularly those studying topology and analysis, as well as educators seeking to clarify concepts related to closed sets and their intersections.

CantorSet
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Hi everyone,

I'm reading Rudin's Analysis and in the topology section, he implies that the finite intersection of closed sets is not necessarily closed. (pg. 34)

Can someone give an example of this? I can't seem to find one.
 
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CantorSet said:
Hi everyone,

I'm reading Rudin's Analysis and in the topology section, he implies that the finite intersection of closed sets is not necessarily closed. (pg. 34)

Can someone give an example of this? I can't seem to find one.

Can you quote what you're reading directly? Because an arbitrary intersection of closed sets is always closed.
 
oops, you're right. I read it wrong.
 

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