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Categorical Interpretations of Absolutes and Extensions

In: Extensions and Absolutes of Hausdorff Spaces

Author

Listed:
  • Jack R. Porter

    (The University of Kansas, Department of Mathematics)

  • R. Grant Woods

    (University of Manitoba, Department of Mathematics)

Abstract

In virtually every branch of abstract mathematics the entities studied are sets endowed with some “structure” (e.g., a topology or a set of algebraic operations), together with “structure-preserving” functions between such sets. It is therefore not surprising that there are many similarities among the various constructions and techniques used in different branches of abstract mathematics, or within a single branch of mathematics. One theme of this book has been the development of a general theory emphasizing the similarities among the various instances of one class of topological constructions, namely extensions. (To a much lesser extent we have studied covers in the same way.) Thus, in Chapter 5, we showed that the Stone-Čech compactification, the maximum zero-dimensional compactification, and the Hewitt realcompactification are all specific examples of the same phenomenon.

Suggested Citation

  • Jack R. Porter & R. Grant Woods, 1988. "Categorical Interpretations of Absolutes and Extensions," Springer Books, in: Extensions and Absolutes of Hausdorff Spaces, chapter 0, pages 691-764, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-3712-9_9
    DOI: 10.1007/978-1-4612-3712-9_9
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