Geometric Topology in Dimensions 2 and 3:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1977
|
| Schriftenreihe: | Graduate Texts in Mathematics
47 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Geometric topology may roughly be described as the branch of the topology of manifolds which deals with questions of the existence of homeomorphisms. Only in fairly recent years has this sort of topology achieved a sufficiently high development to be given a name, but its beginnings are easy to identify. The first classic result was the SchOnflies theorem (1910), which asserts that every 1-sphere in the plane is the boundary of a 2-cell. In the next few decades, the most notable affirmative results were the "Schonflies theorem" for polyhedral 2-spheres in space, proved by J. W. Alexander [Ad, and the triangulation theorem for 2-manifolds, proved by T. Rad6 [Rd. But the most striking results of the 1920s were negative. In 1921 Louis Antoine [A ] published an extraordinary paper in which he 4 showed that a variety of plausible conjectures in the topology of 3-space were false. Thus, a (topological) Cantor set in 3-space need not have a simply connected complement; therefore a Cantor set can be imbedded in 3-space in at least two essentially different ways; a topological 2-sphere in 3-space need not be the boundary of a 3-cell; given two disjoint 2-spheres in 3-space, there is not necessarily any third 2-sphere which separates them from one another in 3-space; and so on and on. The well-known "horned sphere" of Alexander [A ] appeared soon thereafter |
| Beschreibung: | 1 Online-Ressource (X, 262 p) |
| ISBN: | 9781461299066 9781461299080 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/978-1-4612-9906-6 |
Internformat
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| 500 | |a Geometric topology may roughly be described as the branch of the topology of manifolds which deals with questions of the existence of homeomorphisms. Only in fairly recent years has this sort of topology achieved a sufficiently high development to be given a name, but its beginnings are easy to identify. The first classic result was the SchOnflies theorem (1910), which asserts that every 1-sphere in the plane is the boundary of a 2-cell. In the next few decades, the most notable affirmative results were the "Schonflies theorem" for polyhedral 2-spheres in space, proved by J. W. Alexander [Ad, and the triangulation theorem for 2-manifolds, proved by T. Rad6 [Rd. But the most striking results of the 1920s were negative. In 1921 Louis Antoine [A ] published an extraordinary paper in which he 4 showed that a variety of plausible conjectures in the topology of 3-space were false. Thus, a (topological) Cantor set in 3-space need not have a simply connected complement; therefore a Cantor set can be imbedded in 3-space in at least two essentially different ways; a topological 2-sphere in 3-space need not be the boundary of a 3-cell; given two disjoint 2-spheres in 3-space, there is not necessarily any third 2-sphere which separates them from one another in 3-space; and so on and on. The well-known "horned sphere" of Alexander [A ] appeared soon thereafter | ||
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Datensatz im Suchindex
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| author | Moise, Edwin E. |
| author_facet | Moise, Edwin E. |
| author_role | aut |
| author_sort | Moise, Edwin E. |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
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| dewey-search | 514 |
| dewey-sort | 3514 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-9906-6 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:07Z |
| institution | BVB |
| isbn | 9781461299066 9781461299080 |
| issn | 0072-5285 |
| language | English |
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| spelling | Moise, Edwin E. Verfasser aut Geometric Topology in Dimensions 2 and 3 by Edwin E. Moise New York, NY Springer New York 1977 1 Online-Ressource (X, 262 p) txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 47 0072-5285 Geometric topology may roughly be described as the branch of the topology of manifolds which deals with questions of the existence of homeomorphisms. Only in fairly recent years has this sort of topology achieved a sufficiently high development to be given a name, but its beginnings are easy to identify. The first classic result was the SchOnflies theorem (1910), which asserts that every 1-sphere in the plane is the boundary of a 2-cell. In the next few decades, the most notable affirmative results were the "Schonflies theorem" for polyhedral 2-spheres in space, proved by J. W. Alexander [Ad, and the triangulation theorem for 2-manifolds, proved by T. Rad6 [Rd. But the most striking results of the 1920s were negative. In 1921 Louis Antoine [A ] published an extraordinary paper in which he 4 showed that a variety of plausible conjectures in the topology of 3-space were false. Thus, a (topological) Cantor set in 3-space need not have a simply connected complement; therefore a Cantor set can be imbedded in 3-space in at least two essentially different ways; a topological 2-sphere in 3-space need not be the boundary of a 3-cell; given two disjoint 2-spheres in 3-space, there is not necessarily any third 2-sphere which separates them from one another in 3-space; and so on and on. The well-known "horned sphere" of Alexander [A ] appeared soon thereafter Mathematics Topology Mathematik Topologie (DE-588)4060425-1 gnd rswk-swf Geometrische Topologie (DE-588)4156724-9 gnd rswk-swf Geometrie (DE-588)4020236-7 gnd rswk-swf Geometrie (DE-588)4020236-7 s 1\p DE-604 Geometrische Topologie (DE-588)4156724-9 s 2\p DE-604 Topologie (DE-588)4060425-1 s 3\p DE-604 https://doi.org/10.1007/978-1-4612-9906-6 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 |
| spellingShingle | Moise, Edwin E. Geometric Topology in Dimensions 2 and 3 Mathematics Topology Mathematik Topologie (DE-588)4060425-1 gnd Geometrische Topologie (DE-588)4156724-9 gnd Geometrie (DE-588)4020236-7 gnd |
| subject_GND | (DE-588)4060425-1 (DE-588)4156724-9 (DE-588)4020236-7 |
| title | Geometric Topology in Dimensions 2 and 3 |
| title_auth | Geometric Topology in Dimensions 2 and 3 |
| title_exact_search | Geometric Topology in Dimensions 2 and 3 |
| title_full | Geometric Topology in Dimensions 2 and 3 by Edwin E. Moise |
| title_fullStr | Geometric Topology in Dimensions 2 and 3 by Edwin E. Moise |
| title_full_unstemmed | Geometric Topology in Dimensions 2 and 3 by Edwin E. Moise |
| title_short | Geometric Topology in Dimensions 2 and 3 |
| title_sort | geometric topology in dimensions 2 and 3 |
| topic | Mathematics Topology Mathematik Topologie (DE-588)4060425-1 gnd Geometrische Topologie (DE-588)4156724-9 gnd Geometrie (DE-588)4020236-7 gnd |
| topic_facet | Mathematics Topology Mathematik Topologie Geometrische Topologie Geometrie |
| url | https://doi.org/10.1007/978-1-4612-9906-6 |
| work_keys_str_mv | AT moiseedwine geometrictopologyindimensions2and3 |