CRN 11982: HW 6
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Show that a set is LP-compact if and only if it is closed and bounded. | Show that a set is LP-compact if and only if it is closed and bounded. | ||
| − | Hint: | + | Hint: Recall that every bounded infinite set has a limit point. |
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: Recall that every bounded infinite set has a limit point.
