On the continuity of lattice isomorphisms on C(X, I)

Abstract

Abstract We investigate topological conditions on a compact Hausdorff space Y, such that any lattice isomorphism φ : C(X, I) → C(Y, I), where X is a compact Hausdorff space and I is the unit interval [0, 1], is continuous. It is shown that in either of cases that the set of G δ points of Y has a dense pseudocompact subset or Y does not contain the Stone-Čech compactification of ℕ, such a lattice isomorphism is a homeomorphism.