- #1
jeckt
- 19
- 0
Hi All,
This is really a stupid question...I can't seem to get my head around it and it's making me depressed just thinking about it. Anyways, let's consider [tex] \mathbb{R}^{n} [/tex]
the set [tex] S = [0,1] [/tex] is not compact (I know it is but I can't see the flaw in my argument which seems it should be blatantly obvious.) Since [tex] C = \{ (-1,2) \} [/tex] covers [tex] S [/tex] but has no finite subcover (it does and this was pointed out in another thread but they didn't go into detail, I guess because it was so easy). When I say no finite subcover I mean [tex] C_{0} \subset C [/tex] since there is only one element in [tex] C [/tex]
Thanks for the help guys!
This is really a stupid question...I can't seem to get my head around it and it's making me depressed just thinking about it. Anyways, let's consider [tex] \mathbb{R}^{n} [/tex]
the set [tex] S = [0,1] [/tex] is not compact (I know it is but I can't see the flaw in my argument which seems it should be blatantly obvious.) Since [tex] C = \{ (-1,2) \} [/tex] covers [tex] S [/tex] but has no finite subcover (it does and this was pointed out in another thread but they didn't go into detail, I guess because it was so easy). When I say no finite subcover I mean [tex] C_{0} \subset C [/tex] since there is only one element in [tex] C [/tex]
Thanks for the help guys!