Topological spaces and lattices of lower semicontinuous functions
Melvin C. Thornton · Transactions of the American Mathematical Society · 1973
Lower semicontinuous real-valued functions on a space X X form a conditionally complete distributive lattice L ( X ) L(X) . Those lattices which can be represented as L ( X ) L(X) for some X X are characterized algebraically. All spaces producing isomorphic lattices ate determined. The class of spaces which are determined by their function lattices is introduced.