A universal coregular countable second-countable space

A Hausdorff topological space X is called superconnected (resp. coregular ) if for any nonempty open sets U 1 , … n ⊆ the intersection of their closures ‾ ∩ not empty complement ∖ ( a regular space). canonical example projective Q P ∞ vector < ω = { x ∈ : | ≠ 0 } over field rationals . The quotient by equivalence relation ∼ y iff ⋅ We prove that every countable second-countable homeomorphic to subspace and only countable, second-countable, admits decreasing sequence closed such (i) ⋂ ∅ (ii) relatively set closure contains some m (iii) space. Using this characterization we find copies among spaces, orbit spaces group actions, fields.