Supercompactness and Wallman spaces:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam
Math. Centrum
1977
|
| Series: | Mathematisch Centrum <Amsterdam>: Mathematical Centre tracts
85 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IV, 238 S. graph. Darst. |
| ISBN: | 9061961513 |
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MARC
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Record in the Search Index
| _version_ | 1804118845404741632 |
|---|---|
| adam_text | CONTENTS
Preface i
Contents iii
CHAPTER 0 BASIC CONCEPTS 1
[A] General remarks about subbases 1
[b] Some conventions 3
[C] Some definitions 3
[D] Set theoretic axioms 5
CHAPTER I SOPERCOMPACT SPACES 7
1.1. Supercompact spaces 9
1.2. A countable stratifiable space no compact!fication
of which is supercompact 20
1.3. Subbase characterizations of compact topological
spaces 23
1.4. Regular supercompact spaces 43
1.5. Partial orderings on supercompact spaces 49
1.6. Notes 61
CHAPTER II SUPEREXTENSIONS 65
2.1. Linked systems and the Stone representation theorem 67
2.2. Superextensions; some preliminaries 71
2.3. Extending continuous functions to superextensions . 77
2.4. A partial ordering on the set of all
superextensions of a fixed space 86
2.5. Connectedness in superextensions 91
2.6. The dimension of XX 95
2.7. Path connectedness and contractibility of XX. . . . 98
2.8. Subspaces of superextensions; the spaces
a(X) and 2 (X) 106
2.9. Another nonsupercompact compact Hausdorff space . . 123
2.10.Subbases, convex sets and hyperspaces 127
2.11.Notes 140
CHAPTER III INFINITE DIMENSIONAL TOPOLOGY 143
3.1. Metrizability and superextensions 144
3.2. Cell-like mappings and inverse limits 154
3.3. Some X(I,S) is a Hilbert cube 158
3.4. The superextension of the closed unit interval is
homeomorphic to the Hilbert cube 165
3.5. Pseudo-interiors of superextensions 176
3.6. Some subspaces of XX homeomorphic to the
Hilbert cube 183
3.7. Notes 187
CHAPTER IV COMPACTIFICATION THEORY 189
4.1. Wallman compactifications; some preliminaries . . . 190
4.2. Compactifications in which the collection of
multiple points is LindelSf semi-stratifiable . . . 195
4.3. Compactifications of locally compact spaces with
zero-dimensional remainder 201
4.4. Tree-like spaces and Wallman compactifications . . 205
4.5. Regular supercompact superextensions 207
4.6. GA compactifications; some preliminaries 209
4.7. Every compactification of a separable space is
a GA compactification 213
4.8. Notes 218
CHAPTER V A SURVEY OF RECENT RESULTS 221
5.1. Cardinal functions on superextensions 221
5.2. Metrizability in superextensions 221
5.3. The compactness number of a compact topological
space 222
5.4. A cellular constraint in supercompact Hausdorff
spaces 222
5.5. An external characterization of spaces which
admit binary normal subbases 223
5.6. Some elementary proofs in fixed point theory ... 223
5.7. Reductions of the generalized De Groot conjecture. 224
5.8. More about convexity ..... 224
5.9. Convexity preserving mappings in subbase
convexity theory 224
REFERENCES 227
INDEX 235
INDEX OF NAMES 237
|
| any_adam_object | 1 |
| author | Mill, J. van |
| author_facet | Mill, J. van |
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| callnumber-subject | QA - Mathematics |
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| dewey-full | 514/.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514/.3 |
| dewey-search | 514/.3 |
| dewey-sort | 3514 13 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV004727138 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:16:46Z |
| institution | BVB |
| isbn | 9061961513 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002906578 |
| oclc_num | 3950939 |
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| owner | DE-91G DE-BY-TUM DE-29T DE-706 DE-83 DE-188 |
| owner_facet | DE-91G DE-BY-TUM DE-29T DE-706 DE-83 DE-188 |
| physical | IV, 238 S. graph. Darst. |
| psigel | TUB-nveb |
| publishDate | 1977 |
| publishDateSearch | 1977 |
| publishDateSort | 1977 |
| publisher | Math. Centrum |
| record_format | marc |
| series | Mathematisch Centrum <Amsterdam>: Mathematical Centre tracts |
| series2 | Mathematisch Centrum <Amsterdam>: Mathematical Centre tracts |
| spelling | Mill, J. van Verfasser aut Supercompactness and Wallman spaces J. van Mill Amsterdam Math. Centrum 1977 IV, 238 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematisch Centrum <Amsterdam>: Mathematical Centre tracts 85 Supercompact spaces Wallman compactifications Mathematisch Centrum <Amsterdam>: Mathematical Centre tracts 85 (DE-604)BV000893527 85 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002906578&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mill, J. van Supercompactness and Wallman spaces Mathematisch Centrum <Amsterdam>: Mathematical Centre tracts Supercompact spaces Wallman compactifications |
| title | Supercompactness and Wallman spaces |
| title_auth | Supercompactness and Wallman spaces |
| title_exact_search | Supercompactness and Wallman spaces |
| title_full | Supercompactness and Wallman spaces J. van Mill |
| title_fullStr | Supercompactness and Wallman spaces J. van Mill |
| title_full_unstemmed | Supercompactness and Wallman spaces J. van Mill |
| title_short | Supercompactness and Wallman spaces |
| title_sort | supercompactness and wallman spaces |
| topic | Supercompact spaces Wallman compactifications |
| topic_facet | Supercompact spaces Wallman compactifications |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002906578&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT milljvan supercompactnessandwallmanspaces |