fom
Posts:
1,969
Registered:
12/4/12


Re: looking for example of closed set that is *not* complete in a metric space
Posted:
Feb 1, 2013 4:13 PM


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 nonempty > 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. > > > > > > > >

