Maybe I'm missing something obvious here, but doesn't criterion (3) follow from criterion (1)? If that's the case it ought to be stated as a theorem and not part of the definition. (Of course, the reverse implication doesn't hold without a continuity assumption, so these aren't equivalent statements.) --[[User:MarkGall|MarkGall]] 01:06, 31 August 2009 (EDT) | Maybe I'm missing something obvious here, but doesn't criterion (3) follow from criterion (1)? If that's the case it ought to be stated as a theorem and not part of the definition. (Of course, the reverse implication doesn't hold without a continuity assumption, so these aren't equivalent statements.) --[[User:MarkGall|MarkGall]] 01:06, 31 August 2009 (EDT) |