Overview
- Authors:
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Jack R. Porter
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Department of Mathematics, The University of Kansas, Lawrence, USA
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R. Grant Woods
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Department of Mathematics, University of Manitoba, Winnipeg, Canada
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Table of contents (9 chapters)
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Front Matter
Pages i-xiii
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- Jack R. Porter, R. Grant Woods
Pages 1-73
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- Jack R. Porter, R. Grant Woods
Pages 74-154
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- Jack R. Porter, R. Grant Woods
Pages 155-237
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- Jack R. Porter, R. Grant Woods
Pages 238-361
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- Jack R. Porter, R. Grant Woods
Pages 362-439
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- Jack R. Porter, R. Grant Woods
Pages 440-530
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- Jack R. Porter, R. Grant Woods
Pages 531-611
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- Jack R. Porter, R. Grant Woods
Pages 612-690
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- Jack R. Porter, R. Grant Woods
Pages 691-764
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Back Matter
Pages 765-856
About this book
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.
Authors and Affiliations
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Department of Mathematics, The University of Kansas, Lawrence, USA
Jack R. Porter
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Department of Mathematics, University of Manitoba, Winnipeg, Canada
R. Grant Woods
