User talk:Alecscooper/Complete and Close Packed Metric Space is Dense-in-Itself

It appears to me that you need the ordering to be linear, and some relation between ordering and metric, to be able to conclude relevant things. --Lord_Farin (talk) 21:46, 11 December 2012 (UTC)

Possibly, I remember having some really brilliant vision of how these tied together at some point... Total/linear ordering would seem to make sense as a condition at least. And maybe this will finally force me to define an order topology, although I have this feeling that I shouldn't need it/that the relevant properties should fall out of the metric anyway, but that could just be from thinking about everything in terms of $\R$ where all this stuff lines up neatly. Oh well, project for winter break perhaps. --Alec (talk) 06:04, 12 December 2012 (UTC)

The order topology is on my list of stuff to do - it's documented in Steen & Seebach. It will be some while before I get to it though. --prime mover (talk) 06:56, 12 December 2012 (UTC)

So I don't forget where this came from

Based on discussion at Talk:Finite Subspace of Dense-in-itself Metric Space is Not Open --Alec (talk) 21:49, 17 December 2012 (UTC)