Talk:Semimetric space

First-countable
Note: The general semimetric space is not first-countable, and Arkhangekski,Pontryagin provide an explicit counter-example. However, if the space is taken to also be Hausdorff, then Steen and Seebach state that the space is first-countable. This needs to be verified. linas 15:15, 22 November 2006 (UTC)