# Effective Polish space

An effective Polish space is a complete separable metric space X with metric d such that there is a countable dense set C = (c0, c1,...) that makes the following two relations on $\mathbb{N}^4$ computable (Moschovakis 2009:142):
$P(i,j,k,m) \equiv d(c_i,c_j) \leq \frac{m}{k+1}$
$Q(i,j,k,m) \equiv d(c_i,c_j) < \frac{m}{k+1}$