Subject: Morava's question From: Tom Goodwillie Date: Sat, 21 Aug 2004 15:46:27 -0400 To: Don Davis The long line cannot be a topological group. In any connected topological group G a subgroup generated by a neighborhood of the identity must be all of G. On the other hand, the subgroup generated by a compact set must be the union of countably many compact sets. So G if connected and locally compact then it must be the union of countably many compact sets.