7
votes
2answers
635 views

Patching together homeomorphisms: how badly can it fail?

Suppose we have a set $X$ with $X=U \cup V$. If we pick a permutation $f$ of $U$ and a permutation $g$ of $V$ which agree on the intersection $U \cap V$, we can coalesce them into one big endo-map $F$ ...
1
vote
0answers
121 views

Follow up question on the measure of the difference between a partial selector and a selector…

This is a different question from my previous question Difference between a partial selector and a selector, however I am going to repeat the preamble... In Kharazishvili's "Nonmeasurable Sets and ...
0
votes
1answer
137 views

Difference between a partial selector and a selector…

In Kharazishvili's "Nonmeasurable Sets and Functions" there is the following theorem: There exists a subset $X$ of $\mathbb{R}$ which is a Vitali set and a Bernstein set. The proof is as ...
3
votes
1answer
925 views

$\Delta_{2}^{1}$-hard set?

Hello everybody! I'm interested in $\Delta_{2}^{1}$ subsets of Polish spaces, i.e. those sets that are both $\Pi_{2}^{1}$ and $\Sigma_{2}^{1}$ in the boldface hierarchy of Polish spaces. There is a ...