Nonmeasurable Cardinals and Pointfree Topology
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B. Banaschewski
Abstract
This paper establishes that the familiar rôle of nonmeasurable cardinals in classical topology extends to pointfree topology, that is, the setting of frames. For this, it considers the frames which are the pointfree form of the extremally disconnected P-spaces, namely the extremally disconnected 0-dimensional frames in which any countable join of complemented elements is complemented, and shows that they
(1) have discrete spectrum and
(2) are realcompact whenever they have nonmeasurable cardinal.
An important tool obtained for this purpose is the result that, for a Boolean frame L, any σ-frame homomorphism L → 2 preserves the joins of all subsets of nonmeasurable cardinal.
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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
