A NOTE ON RECONSTRUCTION OF SPACES AND MAPS FROM LATTICE DATA

Abstract

Reconstruction of topological spaces from the lattices Ω(X) of open sets, and of continuous maps from lattice homomorphisms satisfying additional properties (formulated in lattice terms) is discussed. We focus on the question when and how the filters λ(x) = {U | x ε U ε (X)} can be specified by algebraic means.