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Literature Cited
A. V. Arkhangel'skii, “Spaces of functions in the pointwise convergence topology and compact spaces,” Usp. Mat. Nauk,39, No. 5, 11–50 (1984).
M. H. Stone, “Application of the theory of Boolean rings to general topology,” Trans. Am. Math. Soc.,41, 375–481 (1937).
I. M. Gel'fand and A. N. Kolmogorov, “On rings of continuous functions on topological spaces,” Dokl. Akad. Nauk SSSR,22, No. 1, 11–15 (1939).
I. Kaplansky, “Lattices of continuous functions,” bull. Am. math. Soc.,53, 613–623 (1947).
I. Shirota, “A generalization of a theorem of I. Kaplansky,” Osaka Math. J.,5, No. 2, 121–132 (1952).
M. Henriksen, “On the equivalence of the ring, lattice and semigroup of continuous functions,” Proc. Am. Math. Soc.,7, 959–960 (1956).
H. Wallman, “Lattice and topological spaces,” Ann. Math.,39, 112–126 (1938).
I. Nagata, “On lattices of functions on topological spaces and of functions on uniform spaces,” Osaka Math. J.,1, No. 2, 166–181 (1949).
J. Thron, “Proximity structures and grills,” Math. Ann.,206, 35–62 (1963).
L. D. Nel, “Lattices of lower semicontinuous functions and associated topological spaces,” Pac. J. Math.,40, No. 3, 667–673 (1972).
L. D. Nel and R. G. Wilson, “Epireflections in the category of To-spaces,” Fund. Math.,75, 69–74 (1972).
W. Govaerts, “A modified notion of E-compactness,” Bull. Acad. Polon. Sci., Ser. Math.,24, No. 1, 61–64 (1972).
R. Nielsen and C. Sloyer, “Ideals of semicontinuous functions and compactifications of T1-spaces,” Math. Ann.,187, No. 4, 329–331 (1970).
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Tiraspol'. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 30, No. 2, pp. 185–191, March–April, 1989.
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Choban, M.M., Kalmutskii, L.I. A theorem of Nagata on lattices of semicontinuous functions. Sib Math J 30, 317–322 (1989). https://doi.org/10.1007/BF00971389
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DOI: https://doi.org/10.1007/BF00971389