Date: Feb 1, 2013 4:13 PM
Author: fom
Subject: Re: looking for example of closed set that is *not* complete in a<br> metric space
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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>

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