Determining whether or not a set is open

  • Thread starter xokaitt
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  • #1
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The problem specifically refers to a set in the complex plane, and since i'm not sure if that belongs here, I will ask this question generally to make sure I have the right idea.


I was given two equations and graphed the intersection. The intersection looks like a three-quarters of a closed ring, not including the first quadrant. All the boundaries except for one are included in the set.

I was asked whether or not the set is open.

I am lead to believe that since you cannot surround a point on one of the included boundaries with an open disk also included in the set, the set is therefore NOT open. But since the set does not contain all its the limit points, it is also not closed... therefore its neither? I'm getting confused.
 

Answers and Replies

  • #2
tiny-tim
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Hi xokaitt! :wink:
I am lead to believe that since you cannot surround a point on one of the included boundaries with an open disk also included in the set, the set is therefore NOT open. But since the set does not contain all its the limit points, it is also not closed... therefore its neither? I'm getting confused.

Yes, some sets are neither open nor closed. :smile:
 
  • #3
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this is a different problem that i'm struggling with , but are you competent in delta-epsilon proofs of continuity?
since ur online and i can maybe take advantage if you are :smile: lol
 
  • #4
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ill post a new thread i guess.
 
  • #5
HallsofIvy
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And, indeed, there are sets that are both open and closed.

And, yes, tiny-tim is very proficient at "epsilon-delta" proofs!
 

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