CRN 11982: HW 6
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HelmutKnaust (Talk | contribs) (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. | + | '''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, | + | '''Problem 28.''' Exercise 3.3.9 (b,e) |
| − | '''Problem 29.''' Exercise | + | '''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 18:40, 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.
