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All the standard material on basic set topology is presented, with the treatment being sometimes new. This is followed by some of the classical, important topological results on Euclidean spaces (the higher-dimensional intermediate value theorem of Poincaré¿Miranda, Brouwer¿s fixed-point theorem, the no-retract theorem, theorems on invariance of domain and dimension, Borsuk¿s antipodal theorem, the Borsuk¿Ulam theorem andthe Lusternik¿Schnirelmann¿Borsuk theorem), all proved by combinatorial methods. This material is not usually found in introductory books on topology. The book concludes with an introduction to homotopy, fundamental groups and covering spaces.
Throughout, original formulations of concepts and major results are provided, along with English translations. Brief accounts of historical developments and biographical sketches of the dramatis personae are provided. Problem solving being an indispensable process of learning, plenty of exercises are provided to hone the reader's mathematical skills. The book would be suitable for a first course in topology and also as a source for self-study for someone desirous of learning the subject. Familiarity with elementary real analysis and some felicity with the language of set theory and abstract mathematical reasoning would be adequate prerequisites for an intelligent study of the book.
All the standard material on basic set topology is presented, with the treatment being sometimes new. This is followed by some of the classical, important topological results on Euclidean spaces (the higher-dimensional intermediate value theorem of Poincaré¿Miranda, Brouwer¿s fixed-point theorem, the no-retract theorem, theorems on invariance of domain and dimension, Borsuk¿s antipodal theorem, the Borsuk¿Ulam theorem andthe Lusternik¿Schnirelmann¿Borsuk theorem), all proved by combinatorial methods. This material is not usually found in introductory books on topology. The book concludes with an introduction to homotopy, fundamental groups and covering spaces.
Throughout, original formulations of concepts and major results are provided, along with English translations. Brief accounts of historical developments and biographical sketches of the dramatis personae are provided. Problem solving being an indispensable process of learning, plenty of exercises are provided to hone the reader's mathematical skills. The book would be suitable for a first course in topology and also as a source for self-study for someone desirous of learning the subject. Familiarity with elementary real analysis and some felicity with the language of set theory and abstract mathematical reasoning would be adequate prerequisites for an intelligent study of the book.
K. Parthasarathy is Former Director and Head of the Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai, India. He earned his doctoral degree from the Indian Institute of Technology Kanpur, after his schooling and college education in Chennai (earlier Madras). His areas of research are abstract harmonic analysis and the theory of frames. He had taught subjects ranging from algebraic number theory to algebraic topology, differential equations to differential geometry and linear algebra to Lie algebras for about 35 years at the postgraduate level at different institutions. He had been Doctoral Adviser for several students and has published a number of research papers in international journals of repute. He is Reviewer for several research journals and for Mathematical Reviews and zbMATH.
Gives proofs of many deep results by using elementary methods
Introduces the Poincare's higher-dimensional intermediate value theorem
Presents the recent Kulpa-Tao proofs of domain and dimension invariance
Erscheinungsjahr: | 2022 |
---|---|
Fachbereich: | Geometrie |
Genre: | Mathematik |
Rubrik: | Naturwissenschaften & Technik |
Medium: | Taschenbuch |
Seiten: | 288 |
Reihe: | La Matematica per il 3+2 |
Inhalt: |
xvii
267 S. 47 s/w Illustr. 267 p. 47 illus. |
ISBN-13: | 9789811694837 |
ISBN-10: | 9811694834 |
Sprache: | Englisch |
Ausstattung / Beilage: | Paperback |
Einband: | Kartoniert / Broschiert |
Autor: | Parthasarathy, K. |
Auflage: | 1st ed. 2022 |
Hersteller: |
Springer Singapore
Springer Nature Singapore La Matematica per il 3+2 |
Maße: | 235 x 155 x 15 mm |
Von/Mit: | K. Parthasarathy |
Erscheinungsdatum: | 10.07.2022 |
Gewicht: | 0,493 kg |
K. Parthasarathy is Former Director and Head of the Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai, India. He earned his doctoral degree from the Indian Institute of Technology Kanpur, after his schooling and college education in Chennai (earlier Madras). His areas of research are abstract harmonic analysis and the theory of frames. He had taught subjects ranging from algebraic number theory to algebraic topology, differential equations to differential geometry and linear algebra to Lie algebras for about 35 years at the postgraduate level at different institutions. He had been Doctoral Adviser for several students and has published a number of research papers in international journals of repute. He is Reviewer for several research journals and for Mathematical Reviews and zbMATH.
Gives proofs of many deep results by using elementary methods
Introduces the Poincare's higher-dimensional intermediate value theorem
Presents the recent Kulpa-Tao proofs of domain and dimension invariance
Erscheinungsjahr: | 2022 |
---|---|
Fachbereich: | Geometrie |
Genre: | Mathematik |
Rubrik: | Naturwissenschaften & Technik |
Medium: | Taschenbuch |
Seiten: | 288 |
Reihe: | La Matematica per il 3+2 |
Inhalt: |
xvii
267 S. 47 s/w Illustr. 267 p. 47 illus. |
ISBN-13: | 9789811694837 |
ISBN-10: | 9811694834 |
Sprache: | Englisch |
Ausstattung / Beilage: | Paperback |
Einband: | Kartoniert / Broschiert |
Autor: | Parthasarathy, K. |
Auflage: | 1st ed. 2022 |
Hersteller: |
Springer Singapore
Springer Nature Singapore La Matematica per il 3+2 |
Maße: | 235 x 155 x 15 mm |
Von/Mit: | K. Parthasarathy |
Erscheinungsdatum: | 10.07.2022 |
Gewicht: | 0,493 kg |