Dual spaces of some congruence lattices. (Q1398186)

The author defines a topological space \(\overline{L_n(X)}\) for any set \(X\) and any \(n\geq 3\). The main result of the paper is a characterization of closed subspaces of \(\overline{L_n(X)}\) for \(| X| \leq\aleph_1\). It turns out that this characterization does not depend on \(n\), which in particular means that any \(\overline{L_n(X)}\) is homeomorphic to a closed subspace of \(\overline{L_3(J)}\) for some topological space \(J\). Also the author discusses the algebraic corollaries of this result.