Isn';t this definition of closed sets flawed?

kindlychung · 发表于 2010-10-1 23:42

What if the set has no limit points or has no Cauchy sequence contained in it?

elimqiu · 发表于 2010-10-2 00:20

[这个贴子最后由elimqiu在 2010/10/01 05:34pm 第 1 次编辑]

Look at set E = {a}, the only sequence made from it is {a(n)} with a(n) = a (n=1,2,...). And it';s a Cauchy sequence.

kindlychung · 发表于 2010-10-2 00:25

In that case E has no limit points, is it closed?

elimqiu · 发表于 2010-10-2 00:33

It has no limit points and so it contains all its limit points. Therefore it is closed

kindlychung · 发表于 2010-10-2 00:46

ok, I see.

wangyangkee · 发表于 2010-10-7 16:38

外文帖子，别往下掉，，，

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Isn';t this definition of closed sets flawed?

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Isn';t this definition of closed sets flawed?

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