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The Boolean Algebra of Regular Open Sets
Published online by Cambridge University Press: 20 November 2018
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Let S be a completely regular topological space. Let C(S) denote the set of bounded, real-valued, continuous functions on 5. It is well known that C(S) forms a distributive lattice under the ordinary pointwise joins and meets. For any distributive lattice L and any ideal I⊆L, a quasi-ordering of L can be defined as follows : f⊇g if, for all h ∈ L, f ∩ h ∈ I implies g ∩ h ∈ I. If equivalent elements under this quasi-ordering are identified, a homomorphic image of L is obtained.
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- Copyright © Canadian Mathematical Society 1953
References
1.
Birkhoff, G., Lattice theory, revised edition (Amer. Math. Soc. Colloquium Publications, vol. 25, 1949).Google Scholar
2.
Dilworth, R. P., The normal completion of the lattice of continuous functions, Trans. Amer. Math. Soc., 68 (1950), 427–438.Google Scholar
3.
Kaplansky, I., Lattices of continuous functions, Bull. Amer. Math. Soc., 53 (1947), 617–622.Google Scholar
4.
Stone, M. H., Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc, 41 (1937), 375–181.Google Scholar
5.
Stone, M. H., Boundedness properties in function-lattices, Can. J. Math., 1 (1949), 176–186.Google Scholar
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