Master of Science
Gulden, Samuel L.
In this paper, it is proved that if the space is a compact Hausdorff space, then the set of real valued continuous functions is also a distributive lattice, where fVg is defined by fVg(x) = f(x)Vg(x) for all x, and f^g is defined similarly. It is also proved that the lattice structure of the set of continuous functions determines the topological spsace up to homeomorphism.
Feissner, George P., "The embedding of pasrtially ordered groups into lattices of continuous functions" (1965). Theses and Dissertations. 3342.