# Lecture Notes on Elementary Topology and Geometry

## Singer, I. M.; Thorpe, J. A.

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At the present time, the average undergraduate mathematics major finds mathematics heavily compartmentalized. After the calculus, he takes a course in analysis and a course in algebra. Depending upon his interests (or those of his department), he takes courses in special topics. Ifhe is exposed to topology, it is usually straightforward point set topology; if he is exposed to geom- etry, it is usually classical differential geometry. The exciting revelations that there is some unity in mathematics, that fields overlap, that techniques of one field have applications in another, are denied the undergraduate. He must wait until he is well into graduate work to see interconnections, presumably because earlier he doesn't know enough. These notes are an attempt to break up this compartmentalization, at least in topology-geometry. What the student has learned in algebra and advanced calculus are used to prove some fairly deep results relating geometry, topol- ogy, and group theory. (De Rham's theorem, the Gauss-Bonnet theorem for surfaces, the functorial relation of fundamental group to covering space, and surfaces of constant curvature as homogeneous spaces are the most note- worthy examples.) In the first two chapters the bare essentials of elementary point set topology are set forth with some hint ofthe subject's application to functional analysis.

Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.

Contenuti:

1 Some point set topology.- 1.1 Naive set theory.- 1.2 Topological spaces.- 1.3 Connected and compact spaces.- 1.4 Continuous functions.- 1.5 Product spaces.- 1.6 The Tychonoff theorem.- 2 More point set topology.- 2.1 Separation axioms.- 2.2 Separation by continuous functions.- 2.3 More separability.- 2.4 Complete metric spaces.- 2.5 Applications.- 3 Fundamental group and covering spaces.- 3.1 Homotopy.- 3.2 Fundamental group.- 3.3 Covering spaces.- 4 Simplicial complexes.- 4.1 Geometry of simplicial complexes.- 4.2 Barycentric subdivisions.- 4.3 Simplicial approximation theorem.- 4.4 Fundamental group of a simplicial complex.- 5 Manifolds.- 5.1 Differentiable manifolds.- 5.2 Differential forms.- 5.3 Miscellaneous facts.- 6 Homology theory and the De Rham theory.- 6.1 Simplicial homology.- 6.2 De Rham’s theorem.- 7 Intrinsic Riemannian geometry of surfaces.- 7.1 Parallel translation and connections.- 7.2 Structural equations and curvature.- 7.3 Interpretation of curvature.- 7.4 Geodesic coordinate systems.- 7.5 Isometries and spaces of constant curvature.- 8 Imbedded manifolds in R3.

Le informazioni nella sezione "Su questo libro" possono far riferimento a edizioni diverse di questo titolo.

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## 1.Lecture Notes on Elementary Topology and Geometry

Editore: Springer, China (2009)
ISBN 10: 0387902023 ISBN 13: 9780387902029
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Descrizione libro Springer, China, 2009. Soft cover. Condizione libro: Brand New. 12mo - over 6¾ - 7¾" tall. International edition Brand New SOFT COVER standard delivery. Codice libro della libreria 001686

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## 2.Lecture Notes on Elementary Topology and Geometry

Editore: Springer-Verlag GmbH, China (2009)
ISBN 10: 0387902023 ISBN 13: 9780387902029
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Descrizione libro Springer-Verlag GmbH, China, 2009. Soft cover. Condizione libro: Brand New. 12mo - over 6¾ - 7¾" tall. International 4edition Brand New SOFT COVER standard delivery. Codice libro della libreria 001396

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## 3.Lecture Notes on Elementary Topology and Geometry (Hardback)

Editore: Springer-Verlag New York Inc., United States (1976)
ISBN 10: 0387902023 ISBN 13: 9780387902029
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Descrizione libro Springer-Verlag New York Inc., United States, 1976. Hardback. Condizione libro: New. Reprint 1976. ed.. 236 x 155 mm. Language: English . Brand New Book. At the present time, the average undergraduate mathematics major finds mathematics heavily compartmentalized. After the calculus, he takes a course in analysis and a course in algebra. Depending upon his interests (or those of his department), he takes courses in special topics. Ifhe is exposed to topology, it is usually straightforward point set topology; if he is exposed to geom- etry, it is usually classical differential geometry. The exciting revelations that there is some unity in mathematics, that fields overlap, that techniques of one field have applications in another, are denied the undergraduate. He must wait until he is well into graduate work to see interconnections, presumably because earlier he doesn t know enough. These notes are an attempt to break up this compartmentalization, at least in topology-geometry. What the student has learned in algebra and advanced calculus are used to prove some fairly deep results relating geometry, topol- ogy, and group theory. (De Rham s theorem, the Gauss-Bonnet theorem for surfaces, the functorial relation of fundamental group to covering space, and surfaces of constant curvature as homogeneous spaces are the most note- worthy examples.) In the first two chapters the bare essentials of elementary point set topology are set forth with some hint ofthe subject s application to functional analysis. Codice libro della libreria SPR9780387902029

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## 4.Lecture Notes On Elementary Topology And Geometry

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Descrizione libro Condizione libro: New. This item is Print on Demand - Depending on your location, this item may ship from the US or UK. Codice libro della libreria POD_9780387902029

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## 5.Lecture Notes on Elementary Topology and Geometry (Hardback)

Editore: Springer-Verlag New York Inc., United States (1976)
ISBN 10: 0387902023 ISBN 13: 9780387902029
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Descrizione libro Springer-Verlag New York Inc., United States, 1976. Hardback. Condizione libro: New. Reprint 1976. ed.. 236 x 155 mm. Language: English . Brand New Book. At the present time, the average undergraduate mathematics major finds mathematics heavily compartmentalized. After the calculus, he takes a course in analysis and a course in algebra. Depending upon his interests (or those of his department), he takes courses in special topics. Ifhe is exposed to topology, it is usually straightforward point set topology; if he is exposed to geom- etry, it is usually classical differential geometry. The exciting revelations that there is some unity in mathematics, that fields overlap, that techniques of one field have applications in another, are denied the undergraduate. He must wait until he is well into graduate work to see interconnections, presumably because earlier he doesn t know enough. These notes are an attempt to break up this compartmentalization, at least in topology-geometry. What the student has learned in algebra and advanced calculus are used to prove some fairly deep results relating geometry, topol- ogy, and group theory. (De Rham s theorem, the Gauss-Bonnet theorem for surfaces, the functorial relation of fundamental group to covering space, and surfaces of constant curvature as homogeneous spaces are the most note- worthy examples.) In the first two chapters the bare essentials of elementary point set topology are set forth with some hint ofthe subject s application to functional analysis. Codice libro della libreria SPR9780387902029

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## 6.Lecture Notes On Elementary Topology And Geometry

ISBN 10: 0387902023 ISBN 13: 9780387902029
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Descrizione libro Condizione libro: New. Depending on your location, this item may ship from the US or UK. Codice libro della libreria 97803879020290000000

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## 7.Lecture Notes on Elementary Topology and Geometry (Undergraduate Texts in Mathematics)

Editore: Springer Verlag (1976)
ISBN 10: 0387902023 ISBN 13: 9780387902029
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Descrizione libro Springer Verlag, 1976. Hardcover. Condizione libro: Brand New. 1st edition. 244 pages. 9.75x6.50x0.75 inches. In Stock. Codice libro della libreria __0387902023

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## 8.Lecture Notes on Elementary Topology and Geometry

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Descrizione libro Springer-Verlag New York Inc., 1976. HRD. Condizione libro: New. New Book. Shipped from US within 10 to 14 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Codice libro della libreria I1-9780387902029

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## 9.Lecture Notes on Elementary Topology and Geometry

Editore: Springer (1976)
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Descrizione libro Springer, 1976. Hardback. Condizione libro: NEW. 9780387902029 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Codice libro della libreria HTANDREE0275104

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## 10.Lecture Notes on Elementary Topology and Geometry (Undergraduate Texts in Mathematics)

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Descrizione libro Springer, 1976. Condizione libro: New. This item is printed on demand for shipment within 3 working days. Codice libro della libreria LP9780387902029

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