Structure of continuous functions of a completely regular space

It is proved that any completely regular topological space is determined up to homeomorphism by the topological lattice (with the topology of pointwise convergence) of all its continuous real-valued functions. The well-known result of Kaplansky (for compact spaces) is a corollary of this theorem.Translated from Matematicheskie Zametki, Vol. 19, No. 6, pp. 863–869, June, 1976.