Geodesic
Structure of continuous functions of a~completely regular space
Matematičeskie zametki, Tome 19 (1976) no. 6, pp. 863-869.

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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. 
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     author = {V. V. Pashenkov},
     title = {Structure of continuous functions of a~completely regular space},
     journal = {Matemati\v{c}eskie zametki},
     pages = {863--869},
     publisher = {mathdoc},
     volume = {19},
     number = {6},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1976_19_6_a5/}
}
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V. V. Pashenkov. Structure of continuous functions of a~completely regular space. Matematičeskie zametki, Tome 19 (1976) no. 6, pp. 863-869. http://geodesic.mathdoc.fr/item/MZM_1976_19_6_a5/