A royal road to topology: convergence of filters
"Topological spaces are a special case of convergence spaces. This textbook introduces topology within a broader context of convergence theory. The title alludes to advantages of the present approach, which is more gratifying than many traditional ones: you travel more comfortably through mathe...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo
World Scientific
[2024]
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Rezension |
| Zusammenfassung: | "Topological spaces are a special case of convergence spaces. This textbook introduces topology within a broader context of convergence theory. The title alludes to advantages of the present approach, which is more gratifying than many traditional ones: you travel more comfortably through mathematical landscapes and you see more. The book is addressed both to those who wish to learn topology and to those who, being already knowledgeable about topology, are curious to review it from a different perspective, which goes well beyond the traditional knowledge. Usual topics of classic courses of set-theoretic topology are treated at an early stage of the book - from a viewpoint of convergence of filters, but in a rather elementary way. Later on, most of these facts reappear as simple consequences of more advanced aspects of convergence theory. The mentioned virtues of the approach stem from the fact that the class of convergences is closed under several natural, essential operations, under which the class of topologies is not! Accordingly, convergence theory complements topology like the field of complex numbers algebraically completes the field of real numbers. Convergence theory is intuitive and operational because of appropriate level of its abstraction, general enough to grasp the underlying laws, but not too much in order not to lose intuitive appeal"-- |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | xxi, 710 Seiten Illustrationen |
| ISBN: | 9789811232107 |
Internformat
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| 100 | 1 | |a Dolecki, Szymon |e Verfasser |0 (DE-588)1112147144 |4 aut | |
| 245 | 1 | 0 | |a A royal road to topology |b convergence of filters |c Szymon Dolecki (Mathematical Institute of Burgundy, Dijon, France) |
| 264 | 1 | |a New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo |b World Scientific |c [2024] | |
| 300 | |a xxi, 710 Seiten |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 520 | 3 | |a "Topological spaces are a special case of convergence spaces. This textbook introduces topology within a broader context of convergence theory. The title alludes to advantages of the present approach, which is more gratifying than many traditional ones: you travel more comfortably through mathematical landscapes and you see more. The book is addressed both to those who wish to learn topology and to those who, being already knowledgeable about topology, are curious to review it from a different perspective, which goes well beyond the traditional knowledge. Usual topics of classic courses of set-theoretic topology are treated at an early stage of the book - from a viewpoint of convergence of filters, but in a rather elementary way. Later on, most of these facts reappear as simple consequences of more advanced aspects of convergence theory. The mentioned virtues of the approach stem from the fact that the class of convergences is closed under several natural, essential operations, under which the class of topologies is not! Accordingly, convergence theory complements topology like the field of complex numbers algebraically completes the field of real numbers. Convergence theory is intuitive and operational because of appropriate level of its abstraction, general enough to grasp the underlying laws, but not too much in order not to lose intuitive appeal"-- | |
| 653 | 0 | |a Topology | |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-035292045 | |
Datensatz im Suchindex
| _version_ | 1828133970490949633 |
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| author | Dolecki, Szymon |
| author_GND | (DE-588)1112147144 |
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| author_sort | Dolecki, Szymon |
| author_variant | s d sd |
| building | Verbundindex |
| bvnumber | BV049954068 |
| classification_tum | MAT 540 |
| ctrlnum | (OCoLC)1446193594 (DE-599)KXP1808434862 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV049954068 |
| illustrated | Illustrated |
| indexdate | 2025-03-31T18:06:54Z |
| institution | BVB |
| isbn | 9789811232107 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-035292045 |
| oclc_num | 1446193594 |
| open_access_boolean | 1 |
| owner | DE-91G DE-BY-TUM |
| owner_facet | DE-91G DE-BY-TUM |
| physical | xxi, 710 Seiten Illustrationen |
| publishDate | 2024 |
| publishDateSearch | 2024 |
| publishDateSort | 2024 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Dolecki, Szymon Verfasser (DE-588)1112147144 aut A royal road to topology convergence of filters Szymon Dolecki (Mathematical Institute of Burgundy, Dijon, France) New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo World Scientific [2024] xxi, 710 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index "Topological spaces are a special case of convergence spaces. This textbook introduces topology within a broader context of convergence theory. The title alludes to advantages of the present approach, which is more gratifying than many traditional ones: you travel more comfortably through mathematical landscapes and you see more. The book is addressed both to those who wish to learn topology and to those who, being already knowledgeable about topology, are curious to review it from a different perspective, which goes well beyond the traditional knowledge. Usual topics of classic courses of set-theoretic topology are treated at an early stage of the book - from a viewpoint of convergence of filters, but in a rather elementary way. Later on, most of these facts reappear as simple consequences of more advanced aspects of convergence theory. The mentioned virtues of the approach stem from the fact that the class of convergences is closed under several natural, essential operations, under which the class of topologies is not! Accordingly, convergence theory complements topology like the field of complex numbers algebraically completes the field of real numbers. Convergence theory is intuitive and operational because of appropriate level of its abstraction, general enough to grasp the underlying laws, but not too much in order not to lose intuitive appeal"-- Topology Convergence Erscheint auch als Online-Ausgabe, ebook for institutions 978-981-123-211-4 Erscheint auch als Online-Ausgabe, ebook for individuals 978-981-123-212-1 DE-601 pdf/application http://www.gbv.de/dms/bowker/toc/9789811232107.pdf 2024-04-28 Aggregator Inhaltsverzeichnis https://zbmath.org/7279531 zbMATH kostenfrei Rezension |
| spellingShingle | Dolecki, Szymon A royal road to topology convergence of filters |
| title | A royal road to topology convergence of filters |
| title_auth | A royal road to topology convergence of filters |
| title_exact_search | A royal road to topology convergence of filters |
| title_full | A royal road to topology convergence of filters Szymon Dolecki (Mathematical Institute of Burgundy, Dijon, France) |
| title_fullStr | A royal road to topology convergence of filters Szymon Dolecki (Mathematical Institute of Burgundy, Dijon, France) |
| title_full_unstemmed | A royal road to topology convergence of filters Szymon Dolecki (Mathematical Institute of Burgundy, Dijon, France) |
| title_short | A royal road to topology |
| title_sort | a royal road to topology convergence of filters |
| title_sub | convergence of filters |
| url | http://www.gbv.de/dms/bowker/toc/9789811232107.pdf https://zbmath.org/7279531 |
| work_keys_str_mv | AT doleckiszymon aroyalroadtotopologyconvergenceoffilters |