Characterization of $\ell_p$-like and $c_0$-like equivalence relations
Longyun Ding · arXiv (Cornell University) · 2010
Let $X$ be a Polish space, $d$ a pseudo-metric on $X$. If $\{(u,v):d(u,v)0$, we show that either $(X,d)$ is separable or there are $δ>0$ and a perfect set $C\subseteq X$ such that $d(u,v)\geδ$ for distinct $u,v\in C$. Granting this dichotomy, we characterize the positions of $\ell_p$-like and $c_0$-like equivalence relations in the Borel reducibility hierarchy.