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The Stone-Čech Compactification / edited by Russell C. Walker.

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Recent research has produced a large number of results concerning the Stone-Cech compactification or involving it in a central manner. The goal of this volume is to make many of these results easily accessible by collecting them in a single source together with the necessary introductory material. T...

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Bibliographic Details
Online Access: Full Text (via Springer)
Main Author: Walker, Russell C.
Format: eBook
Language:English
Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 1974.
Series:Ergebnisse der Mathematik und ihrer Grenzgebiete ; n.F., Heft 83.
Subjects:
Mathematics.
Functional analysis.
Table of Contents:
  • 1. Development of the Stone-?ech Compactification
  • Completely Regular Spaces
  • ?X and the Extension of Mappings
  • ?-Filters and?-Ultrafilters
  • ?X and Maximal Ideal Spaces
  • Spaces of?-Ultrafilters
  • Characterizations of?X
  • Generalizations of Compactness
  • F-Spaces and P-Spaces
  • Other Approaches to?X
  • Exercises
  • 2. Boolean Algebras
  • The Stone Representation Theorem
  • Two Examples
  • The Completion of a Boolean Algebra
  • Separability in Boolean Algebras
  • Exercises
  • 3. On?? and?*
  • The Cardinality of??
  • The Clopen Sets of?? and?*
  • A Characterization of?*
  • Types of Ultrafilters and the Non-Homogeneity of?*
  • Exercises
  • 4. Non-Homogeneity of Growths
  • Types of Points in X*
  • C-Points and C*-Points in X*
  • P-Points in X*
  • Remote Points in X*
  • The Example of??
  • Exercises
  • 5. Cellularity of Growths
  • Lower Bounds for the Cellularity of X*
  • n-Points and Uniform Ultrafilters
  • n-Points and Compactifications of?
  • Exercises
  • 6. Mappings of?X to X*
  • C*-Embedding of Images
  • Retractive Spaces
  • Growths of Compactifications
  • Mappings of?D and other Extremally Disconnected Spaces
  • Exercises
  • 7.?? Revisited
  • ?*\{p} is not Normal
  • An Example Concerning the Banach-Stone Theorem
  • A Point of?* with c Relative Types
  • Types,?*-Types, and P-Points
  • Minimal Types and Points with Finitely Many Relative Types
  • Exercises
  • 8. Product Theorems
  • Glicksberg's Theorem for Finite Products
  • The Product Theorem for Infinite Products
  • Assorted Product Theorems
  • The?-Analogue: An Open Question
  • Exercises
  • 9. Local Connectedness, Continua, and X*
  • Compactifications of Locally Connected Spaces
  • A Non-Metric Indecomposable Continuum
  • Continua as Growths
  • Exercises
  • 10.?X in Categorical Perspective
  • Categories and Functors
  • Reflective Subcategories of the Category of Hausdorff Spaces
  • Adjunctions in Reflective Subcategories
  • Perfect Mappings
  • Projectives
  • Exercises
  • Author Index
  • List of Symbols.

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