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Constructing locales from quantales

Published online by Cambridge University Press:  24 October 2008

Susan B. Niefield  and
Kimmo I. Rosenthal
Susan B. Niefield
Affiliation:
Department of Mathematics, Union College, Schenectady, New York 12308
Kimmo I. Rosenthal
Affiliation:
Department of Mathematics, Union College, Schenectady, New York 12308
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Extract

We recall that a locale is a complete lattice L satisfying a ∧ (∨bα) = ∨(a ∧ bα), for all a ∈ L, and {bα} ⊆ L. Examples of locales include the lattices (X) of open subsets of topological spaces X. Following Joyal and Tierney [7], a morphism f: L → M of locales is a ∨-, ∧-, and τ-preserving map. Such functions are sometimes called ‘frame homomorphisms’, in which case the right adjoint f*:M → L (which exists since f preserves ∨) is then called a ‘morphism of locales’.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 104 , Issue 2 , September 1988 , pp. 215 - 234
Copyright
Copyright © Cambridge Philosophical Society 1988

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