set connected => set closure connected?

kindlychung · 发表于 2010-10-2 20:30

[这个贴子最后由kindlychung在 2010/10/02 08:38pm 第 1 次编辑]

$ \overline{A} $, the set closure of $ A $, means the union of $ A $ and the set of all limit points of $ A $.\

annothing · 发表于 2010-10-2 23:18

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elimqiu · 发表于 2010-10-3 03:44

yes. Actually this in R is very obvious since connected set in R is interval and it';s closure at most adds end points to it.

wangyangkee · 发表于 2010-10-3 07:03

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trx · 发表于 2010-10-3 08:28

kindlychung ，本网网友百分之九九不懂外文，则请外文十分了得的你到专门外文网站去逞雄好不好？！

kindlychung · 发表于 2010-10-3 13:35

yes. Actually this in R is very obvious since connected set in R is interval and it';s closure at most adds end points to it.

Please define "interval" and "end point".

elimqiu · 发表于 2010-10-3 13:54

[a,b],[a,b),(a,b],(a,b)
a,b are endpoints

kindlychung · 发表于 2010-10-3 13:56

[这个贴子最后由kindlychung在 2010/10/03 02:08pm 第 1 次编辑]

What about these?

elimqiu · 发表于 2010-10-3 21:21

they are all true yet the 1st statement is non-trivial.

wangyangkee · 发表于 2010-10-7 16:33

外文帖子，别往下掉，，，

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set connected => set closure connected?

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