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Continuous function sends closed sets on closed sets

  • #1
Let [tex]f: D \rightarrow \mathbb{R}[/tex] be continuous.

Is there an easier function that counterexamples;
if D is closed, then f(D) is closed
than D={2n pi + 1/n: n in N}, f(x)=sin(x) ?????


Plus, these counterexamples are very similar ...but are they correct?

If D is not closed, then f(D) is not closed.
CE: D = (0, 1) and f(x) = 5
If D is not compact, then f(D) is not compact.
CE: We use same CE as above
If D is infinite, then f(D) is infinite.
CE: D = all real numbers and f(x) = 5
If D is an interval, then f(D) is an interval
CE: Use same CE as first
 
Last edited:

Answers and Replies

  • #2
matt grime
Science Advisor
Homework Helper
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Don't double post.
 
  • #3
Couldn't figure out how to delete these mofo's.....so anything to add to my question....?
 

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