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The Boolean Algebra of Regular Open Sets

Published online by Cambridge University Press:  20 November 2018

R. S. Pierce
R. S. Pierce*
Affiliation:
California Institute of Technology
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 5 , 1953 , pp. 95 - 100
Copyright
Copyright © Canadian Mathematical Society 1953

References

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