Notes on the Product of Locales
-
Jorge Picado
and
Aleš Pultr
Abstract
Products of locales (generalized spaces) are coproducts of frames. Because of the algebraic nature of the latter they are often viewed as algebraic objects without much topological connotation. In this paper we first analyze the frame construction emphasizing its tensor product carrier. Then we show how it can be viewed topologically, that is, in the sum-of-the-open-rectangles perspective. The main aim is to present the product from different points of view, as an algebraic and a geometric object, and persuade the reader that both of them are fairly transparent.
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© Mathematical Institute Slovak Academy of Sciences
Articles in the same Issue
- Complexities of Relational Structures
- Notes on the Product of Locales
- Free Objects and Free Extensions in the Category of Frames
- More on Uniform Paracompactness in Pointfree Topology
- Nonmeasurable Cardinals and Pointfree Topology
- Pseudocompact σ-Frames
- Torsion Radicals and Torsion Classes of Cyclically Ordered Groups
- Generalized Commutativity of Lattice-Ordered Groups
- The Relatively Uniform Completion, Epimorphisms and Units, in Divisible Archimedean L-Groups
- Polymorphism-Homogeneous Monounary Algebras
- αcc-Baer Rings
- Pushout Invariance Revisited
- Testing Statistical Hypotheses in Singular Weakly Nonlinear Regression Models
Articles in the same Issue
- Complexities of Relational Structures
- Notes on the Product of Locales
- Free Objects and Free Extensions in the Category of Frames
- More on Uniform Paracompactness in Pointfree Topology
- Nonmeasurable Cardinals and Pointfree Topology
- Pseudocompact σ-Frames
- Torsion Radicals and Torsion Classes of Cyclically Ordered Groups
- Generalized Commutativity of Lattice-Ordered Groups
- The Relatively Uniform Completion, Epimorphisms and Units, in Divisible Archimedean L-Groups
- Polymorphism-Homogeneous Monounary Algebras
- αcc-Baer Rings
- Pushout Invariance Revisited
- Testing Statistical Hypotheses in Singular Weakly Nonlinear Regression Models
