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In this paper the lattice of all real-valued lower semi-continuous functions on a topological space is studied. It is first shown that there is no essential loss if attention is restricted to To-spaces. By suitably topologizing a certain set of equivalence classes of prime ideals, it is shown that a topological space is determined by the lattice. This topological space is homeomorphic with the original space X whenever X has the property that every non-empty irreducible closed set is a pointdoi:10.2140/pjm.1972.40.667 fatcat:j5lju26hhvfh5pd4w7es2hrwke