Talk:Every Filter has Limit Point implies Every Ultrafilter Converges

Following through the definition to the proof here, I have not been able to see any instance where it is necessary to use the fact that $T$ is a topological space. It seems to apply just for filters on general sets. Can this be checked by someone who knows more about this area? --prime mover (talk) 07:15, 2 January 2013 (UTC)

The definitions of limit point and convergent filter rely on topological properties. The only problem I see is the inconsistency wrt language used for topological spaces and their underlying sets. --Dfeuer (talk) 07:27, 2 January 2013 (UTC)

Oh yes of course, so it does. This is one of the reasons why I prefer to use separate symbols for the space and its underlying set - in this case I think it's important to distinguish between the two. --prime mover (talk) 07:41, 2 January 2013 (UTC)