Lectures on non-standard analysis:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1969
|
| Schriftenreihe: | Lecture notes in mathematics
94 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VI, 79 S. |
Internformat
MARC
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| 100 | 1 | |a Machover, Moshé |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Lectures on non-standard analysis |c Moshé Machover ; Joram Hirschfeld |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1969 | |
| 300 | |a VI, 79 S. | ||
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| 490 | 1 | |a Lecture notes in mathematics |v 94 | |
| 650 | 4 | |a Analyse mathématique | |
| 650 | 4 | |a Espaces uniformes | |
| 650 | 4 | |a Logique symbolique et mathématique | |
| 650 | 4 | |a Logic, Symbolic and mathematical | |
| 650 | 4 | |a Mathematical analysis | |
| 650 | 4 | |a Uniform spaces | |
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Datensatz im Suchindex
| _version_ | 1804120467265552384 |
|---|---|
| adam_text | TABLE OF CONTENTS
PAET I - General introduction
by M. Machover
0. The aim of Robinson s theory 1
1. The universe of discourse 2
2. The language /, 5
2.1. Constants, variables and terms 5
2.2. Formulas and sentences 6
3. Standard and non-standard systems 7
3.1. Interpretations ot /, 7
3.2. X and its models 8
3.3. The natural imbedding 9
3.4. Standard and non-standard objects 9
3.5* Internal and external sets 10
3.6. A criterion for internal subsets 11
3.7. Exercises 12
4. Enlargements of U 12
4.1. The compactness theorem 12
4.2. Concurrent relations 14
4.3. Definition and existence of enlargements 14
4.4. Exercises 15
4.5 Special enlargements 16
4.6. Exercise 17
5. Basic topological and metric concepts 17
5.1. Filters 17
5.2. A property of nuclear sets 24
5.3. Topological spaces 25
5.4. Mappings and products 29
5.5. Compact spaces 30
5.6. Non-standard proofs of some standard theorems 32
5.7. Topological groups 34
5.8. Homogeneous spaces 37
VI
5.9- The real line 38
6. Examples 41
6.1. Continuously ordered sets 41
6.2. Powers of continuous segments 42
6.3. A theorem of Kakutani 46
PAET II - Uniform structures
by J. Hirschfeld
7. Uniform spaces 48
7.1. Standard notions 48
7.2. The relation U. 50
7.3- Cauchy filters and approachable points 52
7.4« Completeness and precompactness 55
7.5. The space T^, 56
8. Proximity spaces • • 60
8.1. Standard notions and remarks 60
8.2. Non-standard characterization of proximity relations 61
8.3. Uniform structures and proximity relations • • • 64
9. Functions in uniform and proximity spaces • 68
9.1. Uniformly continuous functions and S -mappings •••••••••• • °8
9.2. Extensions of uniformly continuous functions 70
9.3- Uniformities induced by sets of functions •. 71
9.4- Real functions on topological spaces 75
|
| any_adam_object | 1 |
| author | Machover, Moshé Hirschfeld, Joram |
| author_facet | Machover, Moshé Hirschfeld, Joram |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | QH 150 SI 850 |
| ctrlnum | (OCoLC)600592620 (DE-599)BVBBV006253385 |
| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV006253385 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:42:33Z |
| institution | BVB |
| language | English |
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| physical | VI, 79 S. |
| psigel | HUB-ZB011201007 |
| publishDate | 1969 |
| publishDateSearch | 1969 |
| publishDateSort | 1969 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Machover, Moshé Verfasser aut Lectures on non-standard analysis Moshé Machover ; Joram Hirschfeld Berlin [u.a.] Springer 1969 VI, 79 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 94 Analyse mathématique Espaces uniformes Logique symbolique et mathématique Logic, Symbolic and mathematical Mathematical analysis Uniform spaces Nonstandard-Analysis (DE-588)4137021-1 gnd rswk-swf Nonstandard-Analysis (DE-588)4137021-1 s DE-604 Hirschfeld, Joram Verfasser aut Lecture notes in mathematics 94 (DE-604)BV000676446 94 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003949127&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Machover, Moshé Hirschfeld, Joram Lectures on non-standard analysis Lecture notes in mathematics Analyse mathématique Espaces uniformes Logique symbolique et mathématique Logic, Symbolic and mathematical Mathematical analysis Uniform spaces Nonstandard-Analysis (DE-588)4137021-1 gnd |
| subject_GND | (DE-588)4137021-1 |
| title | Lectures on non-standard analysis |
| title_auth | Lectures on non-standard analysis |
| title_exact_search | Lectures on non-standard analysis |
| title_full | Lectures on non-standard analysis Moshé Machover ; Joram Hirschfeld |
| title_fullStr | Lectures on non-standard analysis Moshé Machover ; Joram Hirschfeld |
| title_full_unstemmed | Lectures on non-standard analysis Moshé Machover ; Joram Hirschfeld |
| title_short | Lectures on non-standard analysis |
| title_sort | lectures on non standard analysis |
| topic | Analyse mathématique Espaces uniformes Logique symbolique et mathématique Logic, Symbolic and mathematical Mathematical analysis Uniform spaces Nonstandard-Analysis (DE-588)4137021-1 gnd |
| topic_facet | Analyse mathématique Espaces uniformes Logique symbolique et mathématique Logic, Symbolic and mathematical Mathematical analysis Uniform spaces Nonstandard-Analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003949127&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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