fom
Posts:
1,039
Registered:
12/4/12
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Re: looking for example of closed set that is *not* complete in a
metric space
Posted:
Feb 1, 2013 4:13 PM
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On 2/1/2013 2:32 PM, fom wrote:
<snip>
Given the attempted care to
detail, the following correction
is probably in order.
>
> To call a subset of a complete space a dense
> subset is to say that such a logical type
> construction could be made from that subset
> to recover the original space.
... to recover an isomorphic copy of the
orginal space.
> The "closeness"
> of a dense subset to its defining space is
> expressed by the fact that it has non-empty
> intersection with every open set of the
> topology.
>
> I think I got all of that right. But, there
> are far more knowledgeable topologists
> in this forum.
>
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