3
votes
0answers
258 views

For METRIZABLE spaces, do the Banach classes and Baire classes coincide?

In this paper: 'Borel structures for Function spaces' by Robert Aumann, http://projecteuclid.org/euclid.ijm/1255631584 Aumann claims that when X and Y are metric spaces (among other things), the ...
3
votes
1answer
284 views

Any subset of Baire space is a union of a boldface $\Delta_2^0$ set and a set with no isolated points. Anybody know how to prove this?

I'm trying to do due diligence and determine whether this is known, trivial, original, etc. I have a proof of: Theorem: If $S\subseteq \mathbb{N}^{\mathbb{N}}$ then $S=X\cup Y$ for some $X$ which is ...
4
votes
3answers
493 views

disjoint translates of a dense uncountable set

If {c(n)} is an arbitrary sequence of irrational numbers converging to 0 then Q + c(n), the set obtained by adding c(n) to the set of rational numbers Q, is clearly disjoint from Q for each n. Is ...