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. > > > > > > > >