Talk:Suslin set

The definition appears to be incorrect. See

www.math.binghamton.edu/dennis/Papers/suslin.pdf

--GL —Preceding unsigned comment added by 195.38.100.34 (talk • contribs) 02:47, 23 December 2006


 * Please be more specific.  What is incorrect? --Aleph4 15:58, 23 December 2006 (UTC)

Incorrect
The article claims that a subset of a Polish space is Suslin if and only if it's analytic. That's not true. The analytic sets are the $$\aleph_0$$-Suslin sets. The $$\aleph_1$$-Suslin sets, just for an example, are the same as the $$\Sigma^1_2$$ sets (projections of co-analytic sets).

It is possible that the claims are true for some older meaning of Suslin set, perhaps for the concept that Suslin originally treated, but they are not for the contemporary meaning.

I am trying to get out the door and don't have time to fix it right now, especially because I'm used to the "tree" definition for Suslin sets, and I'd have to translate to the more general-topology version that's used in this article. (I don't want to shift everything to the tree version if I don't have to, because then you have to do some sort of magic to make it applicable to spaces other than Baire space and Cantor space.) I'll leave some sort of tag on the article. --Trovatore (talk) 19:06, 12 May 2010 (UTC)