Book contents
- Frontmatter
- Dedication
- Epigraph
- Contents
- Preface
- Introduction
- 1 Topological Rings and Modules and Their Completions
- 2 Inverse Limits
- 3 The Idea of Slenderness
- 4 Objects of Type Π / ⨿
- 5 Concrete Examples. Slender Rings
- 6 More Examples of Slender Objects
- Appendix Ordered Sets and Measurable Cardinals
- References
- Notation Index
- Name Index
- Subject Index
1 - Topological Rings and Modules and Their Completions
Published online by Cambridge University Press: 30 November 2018
- Frontmatter
- Dedication
- Epigraph
- Contents
- Preface
- Introduction
- 1 Topological Rings and Modules and Their Completions
- 2 Inverse Limits
- 3 The Idea of Slenderness
- 4 Objects of Type Π / ⨿
- 5 Concrete Examples. Slender Rings
- 6 More Examples of Slender Objects
- Appendix Ordered Sets and Measurable Cardinals
- References
- Notation Index
- Name Index
- Subject Index
Summary
Linear topologies are of utmost importanceComplete objects and metrizable objects play a crucial role in characterizing slenderness.Different kinds of inversesystems, such as surjective, flabby, etc. are introduced here. Product topologies play a central role, as do Hausdorff and non-discrete topologies. Conditions ensuring that infinite sums are contained in an object are investigated.
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- Slenderness , pp. 41 - 90Publisher: Cambridge University PressPrint publication year: 2018