The Normal Completion of the Lattice of Continuous Functions
Dilworth’s paper  on the order completion of the Banach lattice C(S) of all continuous bounded functions on a topological space S was one of the first papers written on this topic and more is known nowadays. It might be worthwhile to follow Dilworth’s ideas in modern terminology and see how a proof of his results could look were this paper written in 1989 instead of 1949.
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- 2.B. Banaschewski, Projective covers in categories of topological spaces and topological algebras, in “Proceedings of the Kanpur Topology Conference, 1968,” Academic Press, New York, 1971, pp. 63–91Google Scholar
- 3.—, Injectivity and essential extensions in equational classes of algebras, in “Proceedings of the Conference on Universal Algebras, Queen’s University, Kingston, Ontario, 1970,” pp. 131-147.Google Scholar
- 5.G. Bruns —, Injective hulls in the category of distributive lattices, J. Reine Angew. Math. 232 (1968), 102–109.Google Scholar
- 6.G. Birkhoff, “Lattice Theory,” 3rd edn., Amer. Math. Soc., Providence, Rhode Island, 1967.Google Scholar
- 12.A.M. Gleason, Projective topological spaces, Illinois J. Math. 2 (1958), 482–489.Google Scholar
- 13.D.B. Goodner, Projections in normed linear spaces, Trans. Amer. Math. Soc. 69 (1950), 89–107.Google Scholar
- 14.P. Halmos, Injective and projective Boolean algebras, in “Lattice Theory,” Proc. Symp. Pure Math., Vol. 2, R.P. Dilworth, ed., Amer. Math. Soc., Providence, Rhode Island, 1961, pp. 114-122.Google Scholar
- 15.—, “Lectures on Boolean Algebras,” Princeton Univ. Press, Princeton, New Jersey, 1963.Google Scholar
- 17.W. Luxemburg and A.C. Zaanen, “Riesz Spaces I/II,” North-Holland, Amsterdam and New York, 1971/1983.Google Scholar
- 23.B. Pareigis, “Kategorien und Funktoren,” Teubner-Verlag, Stuttgart, 1969.Google Scholar
- 26.Z. Semadeni, “Projectivity, Injectivity and Duality,” Rozprawy Matematycyne 35, Warsaw, 1963.Google Scholar
- 27.—, “Banach Spaces of Continuous Functions,” Polish Scientific Publishers, Warsaw, 1971.Google Scholar
- 31.B.C. Vulikh, “Introduction to the Theory of Partially Ordered Vector Spaces,” Wolters-Noordhoff, Groningen, 1967.Google Scholar