CRN 11982: HW 6

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(Created page with "'''Problem 26.''' Exercise 3.3.3 '''Problem 27.''' Exercise 3.3.7 (b,c,e) '''Problem 28.''' Exercise 3.3.9 (b,f) '''Problem 29.''' Exercise 4.2.9 '''Problem 30.''' A set $...")
 
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'''Problem 26.''' Exercise 3.3.3
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'''Problem 26.''' Exercise 3.3.1
  
 
'''Problem 27.''' Exercise 3.3.7 (b,c,e)
 
'''Problem 27.''' Exercise 3.3.7 (b,c,e)
  
'''Problem 28.''' Exercise 3.3.9 (b,f)
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'''Problem 28.''' Exercise 3.3.9 (b,e)
  
'''Problem 29.''' Exercise 4.2.9
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'''Problem 29.''' Exercise 3.3.10
  
 
'''Problem 30.''' A set $X$ is called ''LP-compact'', if every infinite subset $A$ of $X$ has a limit point belonging to $X$.
 
'''Problem 30.''' A set $X$ is called ''LP-compact'', if every infinite subset $A$ of $X$ has a limit point belonging to $X$.

Revision as of 19:40, 28 October 2014

Problem 26. Exercise 3.3.1

Problem 27. Exercise 3.3.7 (b,c,e)

Problem 28. Exercise 3.3.9 (b,e)

Problem 29. Exercise 3.3.10

Problem 30. A set $X$ is called LP-compact, if every infinite subset $A$ of $X$ has a limit point belonging to $X$.

Show that a set is LP-compact if and only if it is closed and bounded.

Hint: Show first that every bounded infinite set has a limit point.

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