The Stone-Čech Compactification
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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| Format: | eBook |
| Language: | English |
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Berlin, Heidelberg
Springer Berlin Heidelberg
1974, 1974
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| Edition: | 1st ed. 1974 |
| Series: | Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge, A Series of Modern Surveys in Mathematics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- Author Index
- List of Symbols
- 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