Talk:Generic point

Closure of a point

The definition talks about the closure of a point, which doesn't make sense to me:

Formally, a generic point is a point P such that every point Q of X is a specialization of P, in the sense of the specialization order (or preorder): the closure of P is the entire set: it is dense.

Is this really correct? —Bromskloss (talk) 13:24, 11 July 2009 (UTC)[reply]

Yes. It's not useful when you have a Hausdorff space, but generic points occur in very different types of space. Charles Matthews (talk) 20:29, 11 July 2009 (UTC)[reply]

contrast

It may be helpful to amplify the introduction by contrasting a generic point and a closed point; then various occurrences of "closed point" (e.g, at Zariski topology) can be linked here. Tkuvho (talk) 17:38, 9 February 2011 (UTC)[reply]

More Examples

It would be good to have more examples, e.g. for a scheme which has several generic points. Spaetzle (talk) 09:22, 20 July 2011 (UTC)[reply]

History

I feel there should be some kind of introductory sentence in the section "history". You somewhat jump right into the story, and as a reader, I don't get the first paragraph at all. What, when, who and why? Seems like there were two concepts at the beginning. Which? And which of them was first? I don't get it.