Extensions and Absolutes of Hausdorff Spaces:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
1988
|
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | 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 |
| Physical Description: | 1 Online-Ressource (XIII, 856p. 27 illus) |
| ISBN: | 9781461237129 9781461283164 |
| DOI: | 10.1007/978-1-4612-3712-9 |
Staff View
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| 500 | |a 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 | ||
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Record in the Search Index
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:06Z |
| institution | BVB |
| isbn | 9781461237129 9781461283164 |
| language | English |
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| spelling | Porter, Jack R. Verfasser aut Extensions and Absolutes of Hausdorff Spaces by Jack R. Porter, R. Grant Woods New York, NY Springer New York 1988 1 Online-Ressource (XIII, 856p. 27 illus) txt rdacontent c rdamedia cr rdacarrier 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 Mathematics Topology Mathematik Hausdorff-Raum (DE-588)4159237-2 gnd rswk-swf Hausdorff-Maß (DE-588)4159238-4 gnd rswk-swf Topologischer Raum (DE-588)4137586-5 gnd rswk-swf Hausdorff-Kompaktifizierung (DE-588)4159235-9 gnd rswk-swf Topologischer Raum (DE-588)4137586-5 s 1\p DE-604 Hausdorff-Raum (DE-588)4159237-2 s 2\p DE-604 Hausdorff-Kompaktifizierung (DE-588)4159235-9 s 3\p DE-604 Hausdorff-Maß (DE-588)4159238-4 s 4\p DE-604 Woods, R. Grant Sonstige oth https://doi.org/10.1007/978-1-4612-3712-9 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Porter, Jack R. Extensions and Absolutes of Hausdorff Spaces Mathematics Topology Mathematik Hausdorff-Raum (DE-588)4159237-2 gnd Hausdorff-Maß (DE-588)4159238-4 gnd Topologischer Raum (DE-588)4137586-5 gnd Hausdorff-Kompaktifizierung (DE-588)4159235-9 gnd |
| subject_GND | (DE-588)4159237-2 (DE-588)4159238-4 (DE-588)4137586-5 (DE-588)4159235-9 |
| title | Extensions and Absolutes of Hausdorff Spaces |
| title_auth | Extensions and Absolutes of Hausdorff Spaces |
| title_exact_search | Extensions and Absolutes of Hausdorff Spaces |
| title_full | Extensions and Absolutes of Hausdorff Spaces by Jack R. Porter, R. Grant Woods |
| title_fullStr | Extensions and Absolutes of Hausdorff Spaces by Jack R. Porter, R. Grant Woods |
| title_full_unstemmed | Extensions and Absolutes of Hausdorff Spaces by Jack R. Porter, R. Grant Woods |
| title_short | Extensions and Absolutes of Hausdorff Spaces |
| title_sort | extensions and absolutes of hausdorff spaces |
| topic | Mathematics Topology Mathematik Hausdorff-Raum (DE-588)4159237-2 gnd Hausdorff-Maß (DE-588)4159238-4 gnd Topologischer Raum (DE-588)4137586-5 gnd Hausdorff-Kompaktifizierung (DE-588)4159235-9 gnd |
| topic_facet | Mathematics Topology Mathematik Hausdorff-Raum Hausdorff-Maß Topologischer Raum Hausdorff-Kompaktifizierung |
| url | https://doi.org/10.1007/978-1-4612-3712-9 |
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