Introduction to topology and modern analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Malabar, Fla.
Krieger
1983
|
| Ausgabe: | Repr. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 372 S. |
| ISBN: | 0898745519 |
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Datensatz im Suchindex
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| adam_text | Titel: Introduction to topology and modern analysis
Autor: Simmons, George Finlay
Jahr: 1983
Contents Preface vii A Note to the Reader xi PART ONE: TOPOLOGY Chapter One SETS AND FUNCTIONS 3 1. Sets and set inclusion 3 2. The algebra of sets 7 3. Functions 14 4. Products of sets 21 5. Partitions and equivalence relations 25 6. Countable sets 31 7. Uncountable sets 36 8. Partially ordered sets and lattices 43 Chapter Two METRIC SPACES 49 9. The definition and some examples 51 10. Open sets 59 11. Closed sets 65 12. Convergence, completeness, and Baire’s theorem 70 13. Continuous mappings 75 14. Spaces of continuous functions 80 15. Euclidean and unitary spaces 85 Chapter Three TOPOLOGICAL SPACES 91 16. The definition and some examples 92 17. Elementary concepts 95 18. Open bases and open subbases 99 19. Weak topologies 104 20. The function algebras e(X,R ) and e(X,C) 106 Chapter Four COMPACTNESS 110 21. Compact spaces 111 22. Products of spaces 115 xiil
xlv Contents 23. Tychonoff’s theorem and locally compact spaces 118 24. Compactness for metric spaces 120 25. Ascoli’s theorem 124 Chapter Five SEPARATION 129 26. 7 ’ 1 -spaces and Hausdorff spaces 130 27. Completely regular spaces and normal spaces 132 28. Urysohn’s lemma and the Tietze extension theorem 135 29. The Urysohn imbedding theorem 137 30. The Stone-Öech compactification 139 Chapter Six CONNECTEDNESS 142 31. Connected spaces 143 32. The components of a space 146 33. Totally disconnected spaces 149 34. Locally connected spaces 150 Chapter Seven APPROXIMATION 153 35. The Weierstrass approximation theorem 153 36. The Stone-Weierstrass theorems 157 37. Locally compact Hausdorff spaces 162 38. The extended Stone-Weierstrass theorems 165 PART TWO: OPERATORS Chapter Eight ALGEBRAIC SYSTEMS 171 39. Groups 172 40. Rings 181 41. The structure of rings 184 42. Linear spaces 191 43. The dimension of a linear space 196 44. Linear transformations 203 45. Algebras 208 Chapter Nine BANACH SPACES 211 46. The definition and some examples 212 47. Continuous linear transformations 219 48. The Hahn-Banach theorem 224 49. The natural imbedding of N in N ** 231 50. The open mapping theorem 235 51. The conjugate of an operator 239 Chapter Ten HILBERT SPACES 243 52. The definition and some simple properties 244 53. Orthogonal complements 249 54. Orthonormal sets 251
Contents xv 55. The conjugate space H* 260 56. The adjoint of an operator 262 57. Self-adjoint operators 266 58. Normal and unitary operators 269 59. Projections 273 Chapter Eleven FINITE-DIMENSIONAL SPECTRAL THEORY 278 60. Matrices 280 61. Determinants and the spectrum of an operator 287 62. The spectral theorem 290 63. A survey of the situation 295 PART THREE: ALGEBRAS OF OPERATORS Chapter Twelve GENERAL PRELIMINARIES ON BANACH ALGEBRAS 301 64. The definition and some examples 302 65. Regular and singular elements 305 66. Topological divisors of zero 307 67. The spectrum 308 68. The formula for the spectral radius 312 69. The radical and semi-simplicity 313 Chapter Thirteen THE STR UCTURE OF COMM UTA TIVE BANACH ALGEBRAS 318 70. The Gelfand mapping 318 71. Applications of the formula r(x) = lim ||z*|| 1/ * 323 72. Involutions in Banach algebras 324 73. The Gelfand-Neumark theorem 325 Chapter Fourteen SOME SPECIAL COMMUTA TIVE BANACH ALGEBRAS 327 74. Ideals in C(X) and the Banach-Stone theorem 327 75. The Stone-Ôech compactification (continued) 330 76. Commutative C‘-algebras 332 APPENDICES ONE Fixed point theorems and some applications to analysis 337 TWO Continuous curves and the Hahn-Mazurkiewicz theorem 341 THREE Boolean algebras, Boolean rings, and Stone’s theorem 344 Bibliography Index of Symbols Subject Index 355 359 363
|
| any_adam_object | 1 |
| author | Simmons, George Finlay 1925-2019 |
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| discipline | Mathematik |
| edition | Repr. ed. |
| format | Book |
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| spellingShingle | Simmons, George Finlay 1925-2019 Introduction to topology and modern analysis Topologischer Vektorraum (DE-588)4122383-4 gnd Analysis (DE-588)4001865-9 gnd Operatoralgebra (DE-588)4129366-6 gnd Topologie (DE-588)4060425-1 gnd Operator (DE-588)4130529-2 gnd Banach-Algebra (DE-588)4193187-7 gnd |
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| title | Introduction to topology and modern analysis |
| title_auth | Introduction to topology and modern analysis |
| title_exact_search | Introduction to topology and modern analysis |
| title_full | Introduction to topology and modern analysis George F. Simmons |
| title_fullStr | Introduction to topology and modern analysis George F. Simmons |
| title_full_unstemmed | Introduction to topology and modern analysis George F. Simmons |
| title_short | Introduction to topology and modern analysis |
| title_sort | introduction to topology and modern analysis |
| topic | Topologischer Vektorraum (DE-588)4122383-4 gnd Analysis (DE-588)4001865-9 gnd Operatoralgebra (DE-588)4129366-6 gnd Topologie (DE-588)4060425-1 gnd Operator (DE-588)4130529-2 gnd Banach-Algebra (DE-588)4193187-7 gnd |
| topic_facet | Topologischer Vektorraum Analysis Operatoralgebra Topologie Operator Banach-Algebra Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019641110&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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