
#1
Mar2312, 03:06 PM

P: 23

the definition of limit point:
a point p is a limit point of E(subset of metric space X) if every neighborhood of p contains a point q≠p which is in E. My question is that is there a limit point p which is not in E? 



#2
Mar2312, 03:10 PM

P: 799





#3
Mar2312, 03:31 PM

P: 23

can you give me an example of a set that is perfect? def: E is perfect if E is closed and if every point of E is a limit point of E 



#4
Mar2312, 03:59 PM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 38,904

about limit point
So you refuse to answer SteveL27's question?
But I will answer your question: [0, 1]. It's actually harder to give an example of a closed set that is NOT perfect. Can you? 



#5
Mar2512, 02:11 PM

P: 134





#6
Mar2512, 07:24 PM

P: 192

(0, 1] is not closed; it's just also not open. A good example of a closed nonperfect set is one with an isolated point, like {2}, or [0,1][itex]\cup[/itex]{2}.



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