Talk:Sequentially Compact Metric Space is Lindelöf

This argument basically shows that a second-countable space is Lindelöf. Maybe this proof can be included as a second proof that a second-countable space is Lindelöf, and this page can just be reduced to the statement that a sequentially compact metric space is second-countable and a second-countable space is Lindelöf? Abcxyz 00:37, 16 March 2012 (EDT)