Topological Spaces: From Distance to Neighborhood
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1997
|
| Schriftenreihe: | Undergraduate Texts in Mathematics
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book is a text, not a reference, on Point-set Thpology. It addresses itself to the student who is proficient in Calculus and has some experience with mathematical rigor, acquired, e.g., via a course in Advanced Calculus or Linear Algebra. Th most beginners, Thpology offers a double challenge. In addition to the strangeness of concepts and techniques presented by any new subject, there is an abrupt rise of the level of abstraction. It is a bad idea to teach a student two things at the same moment. Th mitigate the culture shock, we move from the special to the general, dividing the book into three parts: 1. The Line and the Plane 2. Metric Spaces 3. Thpological Spaces. In this way, the student has ample time to get acquainted with new ideas while still on familiar territory. Only after that, the transition to a more abstract point of view takes place. Elementary Thpology preeminently is a subject with an extensive ar ray of technical terms indicating properties of topological spaces. In the main body of the text, we have purposely restricted our mathematical vocabulary as much as is reasonably possible. Such an enterprise is risky. Doubtlessly, many readers will find us too thrifty. Th meet them halfway, in Chapter 18 we briefly introduce and discuss a number of topological properties, but even there we do not touch on paracompactness, com plete normality, and extremal disconnectedness-just to mention three terms that are not really esoteric |
| Beschreibung: | 1 Online-Ressource (XI, 313 p) |
| ISBN: | 9781461206651 9781461268628 |
| ISSN: | 0172-6056 |
| DOI: | 10.1007/978-1-4612-0665-1 |
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Datensatz im Suchindex
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| author | Buskes, Gerard |
| author_facet | Buskes, Gerard |
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| bvnumber | BV042419588 |
| classification_tum | MAT 000 |
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| ctrlnum | (OCoLC)863758887 (DE-599)BVBBV042419588 |
| dewey-full | 514 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514 |
| dewey-search | 514 |
| dewey-sort | 3514 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-0665-1 |
| format | Electronic eBook |
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| id | DE-604.BV042419588 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:05Z |
| institution | BVB |
| isbn | 9781461206651 9781461268628 |
| issn | 0172-6056 |
| language | English |
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| spelling | Buskes, Gerard Verfasser aut Topological Spaces From Distance to Neighborhood by Gerard Buskes, Arnoud Rooij New York, NY Springer New York 1997 1 Online-Ressource (XI, 313 p) txt rdacontent c rdamedia cr rdacarrier Undergraduate Texts in Mathematics 0172-6056 This book is a text, not a reference, on Point-set Thpology. It addresses itself to the student who is proficient in Calculus and has some experience with mathematical rigor, acquired, e.g., via a course in Advanced Calculus or Linear Algebra. Th most beginners, Thpology offers a double challenge. In addition to the strangeness of concepts and techniques presented by any new subject, there is an abrupt rise of the level of abstraction. It is a bad idea to teach a student two things at the same moment. Th mitigate the culture shock, we move from the special to the general, dividing the book into three parts: 1. The Line and the Plane 2. Metric Spaces 3. Thpological Spaces. In this way, the student has ample time to get acquainted with new ideas while still on familiar territory. Only after that, the transition to a more abstract point of view takes place. Elementary Thpology preeminently is a subject with an extensive ar ray of technical terms indicating properties of topological spaces. In the main body of the text, we have purposely restricted our mathematical vocabulary as much as is reasonably possible. Such an enterprise is risky. Doubtlessly, many readers will find us too thrifty. Th meet them halfway, in Chapter 18 we briefly introduce and discuss a number of topological properties, but even there we do not touch on paracompactness, com plete normality, and extremal disconnectedness-just to mention three terms that are not really esoteric Mathematics Topology Mathematik Topologischer Raum (DE-588)4137586-5 gnd rswk-swf Topologischer Raum (DE-588)4137586-5 s 1\p DE-604 Rooij, Arnoud Sonstige oth https://doi.org/10.1007/978-1-4612-0665-1 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Buskes, Gerard Topological Spaces From Distance to Neighborhood Mathematics Topology Mathematik Topologischer Raum (DE-588)4137586-5 gnd |
| subject_GND | (DE-588)4137586-5 |
| title | Topological Spaces From Distance to Neighborhood |
| title_auth | Topological Spaces From Distance to Neighborhood |
| title_exact_search | Topological Spaces From Distance to Neighborhood |
| title_full | Topological Spaces From Distance to Neighborhood by Gerard Buskes, Arnoud Rooij |
| title_fullStr | Topological Spaces From Distance to Neighborhood by Gerard Buskes, Arnoud Rooij |
| title_full_unstemmed | Topological Spaces From Distance to Neighborhood by Gerard Buskes, Arnoud Rooij |
| title_short | Topological Spaces |
| title_sort | topological spaces from distance to neighborhood |
| title_sub | From Distance to Neighborhood |
| topic | Mathematics Topology Mathematik Topologischer Raum (DE-588)4137586-5 gnd |
| topic_facet | Mathematics Topology Mathematik Topologischer Raum |
| url | https://doi.org/10.1007/978-1-4612-0665-1 |
| work_keys_str_mv | AT buskesgerard topologicalspacesfromdistancetoneighborhood AT rooijarnoud topologicalspacesfromdistancetoneighborhood |