Topology (eBook)

Volume II

K. Kuratowski (Autor)

eBook Download: PDF

2014 | 1. Auflage
622 Seiten
Elsevier Science (Verlag)
978-1-4832-7179-8 (ISBN)

Infos

Topology, Volume II deals with topology and covers topics ranging from compact spaces and connected spaces to locally connected spaces, retracts, and neighborhood retracts. Group theory and some cutting problems are also discussed, along with the topology of the plane. Comprised of seven chapters, this volume begins with a discussion on the compactness of a topological space, paying particular attention to Borel, Lebesgue, Riesz, Cantor, and Bolzano-Weierstrass conditions. Semi-continuity and topics in dimension theory are also considered. The reader is then introduced to the connectedness of a space, with emphasis on the general properties and monotone mappings of connected spaces; local connectedness of a topological space; absolute retracts and contractible spaces; and general properties of commutative groups. Qualitative problems related to polygonal arcs are also examined, together with cohomotopic multiplication and duality theorems. The final chapter is devoted to the topology of a plane and evaluates the concept of the Janiszewski space. This monograph will be helpful to students and practitioners of algebra and mathematics.

Inhalt

Front Cover 1
Topology 4
Copyright Page 5
Table of Contents 10
Dedication 6
PREFACE TO THE SECOND VOLUME 8
CHAPTER FOUR. COMPACT SPACES 16
41. Compactness 16
42. The 
60 
43. Semi-continuity 72
44, The 
90 
45. Topics in dimension theory (continued) 111
CHAPTEE FIVE. CONNECTED SPACES 142
46. Connectedness 142
47. Continua 182
48. Irreducible spaces. Indecomposable spaces 205
CHAPTEK SIX. LOCALLY CONNECTED SPACES 242
49. Local connectedness 242
50. Locally connected metric continua 267
51. Theory of curves. The order of a space at a point 289
52. Cyclic elements of a locally connected metric continuum 322
CHAPTER SEVEN. ABSOLUTE RETRACTS. SPACES CONNECTED IN DIMENSION n CONTRACTIBLE SPACES 347
53. Extending of continuous functions. Eetraction 347
54. Homotopy. Contractibility 375
CHAPTER EIGHT. 
400 
55. 
400 
56. The 
421 
57. Spaces contractible with respect to 
449 
58. The 
458 
CHAPTER NINE. SOME THEOREMS ON THE DISCONNECTION OF THE 
476 
59. Qualitative problems 476
60. Quantitative problems. Cohomotopic multiplication Duality theorems 494
CHAPTER TEN. TOPOLOGY OF THE PLANE 520
61. Qualitative problems 520
62. Quantitative problems. The 
557 
List of important symbols 610
Author index 612
Subject index 617

Produkt-Details

• Erscheint lt. Verlag: 12.5.2014
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Themenwelt: Technik
• ISBN-10: 1-4832-7179-X / 148327179X
• ISBN-13: 978-1-4832-7179-8 / 9781483271798