The Stone-Cech Compactification

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.