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Extensions and Absolutes of Hausdorff Spaces

  • Jack R. Porter
  • R. Grant Woods

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Jack R. Porter, R. Grant Woods
    Pages 1-73
  3. Jack R. Porter, R. Grant Woods
    Pages 74-154
  4. Jack R. Porter, R. Grant Woods
    Pages 155-237
  5. Jack R. Porter, R. Grant Woods
    Pages 238-361
  6. Jack R. Porter, R. Grant Woods
    Pages 362-439
  7. Jack R. Porter, R. Grant Woods
    Pages 440-530
  8. Jack R. Porter, R. Grant Woods
    Pages 531-611
  9. Jack R. Porter, R. Grant Woods
    Pages 612-690
  10. Jack R. Porter, R. Grant Woods
    Pages 691-764
  11. Back Matter
    Pages 765-856

About this book

Introduction

An extension of a topological space X is a space that contains X as a dense subspace. The construction of extensions of various sorts - compactifications, realcompactifications, H-elosed extension- has long been a major area of study in general topology. A ubiquitous method of constructing an extension of a space is to let the "new points" of the extension be ultrafilters on certain lattices associated with the space. Examples of such lattices are the lattice of open sets, the lattice of zero-sets, and the lattice of elopen sets. A less well-known construction in general topology is the "absolute" of a space. Associated with each Hausdorff space X is an extremally disconnected zero-dimensional Hausdorff space EX, called the Iliama absolute of X, and a perfect, irreducible, a-continuous surjection from EX onto X. A detailed discussion of the importance of the absolute in the study of topology and its applications appears at the beginning of Chapter 6. What concerns us here is that in most constructions of the absolute, the points of EX are certain ultrafilters on lattices associated with X. Thus extensions and absolutes, although very different, are constructed using similar tools.

Keywords

Compactification Extensions Hausdorff Spaces topology

Authors and affiliations

  • Jack R. Porter
    • 1
  • R. Grant Woods
    • 2
  1. 1.Department of MathematicsThe University of KansasLawrenceUSA
  2. 2.Department of MathematicsUniversity of ManitobaWinnipegCanada

Bibliographic information