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.
@article{MZM_1976_19_6_a5,
author = {V. V. Pashenkov},
title = {Structure of continuous functions of a~completely regular space},
journal = {Matemati\v{c}eskie zametki},
pages = {863--869},
year = {1976},
volume = {19},
number = {6},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1976_19_6_a5/}
}
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/