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Cairns S.S. — Introductory topology
Cairns S.S. — Introductory topology

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Название: Introductory topology

Автор: Cairns S.S.

Аннотация:

This book is the culmination of repeatedly revised sets of class notes used by the author in teaching introductory topology courses. Its purpose is to progress as far as practicable into the fundamental concepts and the principal results of homology theory, both in their combinatorial development and in their application to topological spaces.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1961

Количество страниц: 256

Добавлена в каталог: 25.11.2012

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abelian      (see Group)
Adjacent      112
Affine transformation      68
Aggregate      41
Alexander duality theorem      180
Approximating complex      143
Approximating simplex      143
ARC      186
Arithmetical continuum      48
Barycenter      73 83
Barycentric coordinates      70
Barycentric subdivision      83
Base, Betti      119
Base, connectivity      122
Base, homology      119
Base, of a topology      52
Base, torsion      119
Basis      222
Betti, base      119
Betti, group      97
Betti, number      7 97 228
Betti, relative (or mod L)      176
Betti, singular      132
Bolzano — Weierstrass theorem      59
Boundary of a chain      94
Boundary of a set      53
Boundary of a simplex      72
Boundary of a surface      15
Boundary, chain      92
Boundary, complex      100
Boundary, face      77
Boundary, mod      2 121
Boundary, point      53
Boundary, simplex      72
Bounded      57
Brouwer dimension      62 136
Brouwer’s fixed-point theorem      137
Carrier      133
Cell, abstract      78
Cell, boundary of      87
Cell, chain      165
Cell, complex      165
Cell, dimension of      78
Cell, face of      87
Cell, homology      165
Cell, polyhedral      87
Chain      92
Chain of a complex      112
Chain, boundary of      92 94
Chain, cell      165
Chain, coboundary      122
Chain, equality of      130
Chain, group      92 95
Chain, singular      130
Characteristic      109 118
Characteristic, mod L      177
Circuit      6
class      41
Class of mappings      152
Class, equivalence      44
Class, residue      218
Closed interval      48
Closed mapping      55
Closed set      53
Closed surface      15
Closure      53
Coboundary      123
Coboundary, chain      122
Coboundary, operator      122
Cocycle      123
Coherently oriented      93 112
Cohomology, class      124
Cohomology, group      124
Cohomology-independent      125
Collection      41
Column vector      223
Combinatorial equivalence      83 88
Combinatorial homotopy      195
Compact      59
Compactum      59
Complement      42
COMPLEX      74
Complex of a chain      142
Complex, abstract      77
Complex, boundary      100
Complex, cell      165
Complex, cone      154
Complex, denumerable      77
Complex, dimension of      77
Complex, finite      74 77
Complex, floor      145
Complex, generalized      78
Complex, infinite      75
Complex, isomorphic      80
Complex, linear      77
Complex, oriented      92
Complex, polyhedral      87
Complex, realization of      78
Complex, roof      145
Complex, singular      142
Complex, subdivision of      87
Complex, topological      76
Component      76 77
Components, contra variant      231
Components, covariant      232
Composition of mappings      43
Cone complex      154
Congruent mod      220
Congruent mod m      218
Connected      76 77
Connected graph      4
Connected surface      15
Connected, arc wise      187
Connected, simply      191
Connectivity, base      122
Connectivity, group      121
Connectivity, number      121
Continuity      51
continuous      49 50 51
Continuous at a point      54
continuous curve      185
Continuous on a space      54
Continuum      48
Converge      54
Convex      66
Coordinates, affine      68
Coordinates, barycentric      70
Coordinates, rectangular Cartesian      68
Coordinates, skew      68
Coset      220
Countable      44
Cover      205 209
Covering      59
Covering complex, universal      210
Covering pair      177
Covering path      209
Covering set      205
Covering space      205
Covering, $\eta$-covering      61
Covering, closed      59
Covering, infinite      205
Covering, k-fold      205
Covering, of mesh $\eta$      61
Covering, open      59
Covering, order of      62
Covering, simple      64
Crosscap      22
Curve, closed      186
Curve, Peano      186
Curve, simple      186
CYCLE      94
Cycle, group      94 95
Cyclomatic number      7
Decomposition      45
Deformation      152 187
Deformation, homotopic      151
Deformation, path      151
Denumerable      43
Diagonal      136
Diameter      57
DIMENSION      65
Dimension, Brouwer      62 136
Dimension, number      65 67
Dimension, numerical      67
Disjoint      42
Distance, between two sets      57
Distance, Euclidean      50
Domain      42
Dual bases      233
Dual homomorphisms      235
Duality theorem, Alexander      180
Duality theorem, Lefschetz      179
Duality theorem, Poincare      173
EDGE      19
Edge, free      19
Edge, paired      19
Edge, path      193
Empty      41
Equivalence, class      44
Equivalence, combinatorial      83 88
Equivalence, relation      44
Euclidean space      48 50
Euler — Poincare characteristic      109 118
Euler’s theorem      12
Extension      42
Face      77
Face of a simplex      72
Face, boundary      77
Factor group      220
Fixed point      136
Fixed-point theorem      137
Floor complex      145
Function      (see Mapping)
Fundamental group      185 189 190 196
Genus      109
Graph      4
Graph of a function      51 136
Graph of a relation      45
Graph, connected      4
Graph, linear      4
Group of order m      218
Group, abelian      215
Group, addition      215
Group, additive      215
Group, axioms      215
Group, basis      222
Group, Betti      97 176
Group, bounding cycle      95 166
Group, chain      92 95
Group, cobounding cocycle      166
Group, cocycle      166
Group, cohomology      124 166
Group, combinatorial      196
Group, commutative      215
Group, connectivity      121
Group, cycle      94 95 165 166
Group, cyclic      218
Group, difference      220
Group, factor      220
Group, finitely generated      216
Group, free abelian      217
Group, free cyclic      218
Group, free multiplicative      217
Group, fundamental      185 187 189 190
Group, generators      216
Group, homology      96 166
Group, invariant      219
Group, inverse element      215
Group, local      159
Group, made abelian      196
Group, mod      2 121
Group, multiplication      215
Group, multiplicative      215
Group, Poincare      (see Group fundamental)
Group, product, direct      221
Group, quotient      220
Group, relations      217
Group, relative (or mod L)      176
Group, relative cycle      176
Group, singular      132
Group, structure      219
Group, torsion relative      176
Group, unit element      215
Half-space      86 111
Half-space, closed      86
Half-space, open      86
Handle      25
Heine — Borel theorem      60
Homeomorphic      54
Homeomorphism      54 55
Homeomorphism, linear      69
Homologous      96
Homology, base      119
Homology, cell      165
Homology, class      96
Homology, group      96
Homology, relative      175
Homology, singular      131
Homology-independent      97
Homomorphism      219
Homomorphism, dual      235
Homotopic, chains      152
Homotopic, complexes      152
Homotopy      152
Homotopy, class      152 189 196
Homotopy, combinatorial      195
Image      42
incidence      77
Incidence, matrix      114
Incidence, normal      115
Incidence, number      114 165
Incidence, relation      77
incident      17 75
Independent, cohomology      125
Independent, homology      97
Independent, linearly      71 97
Induced homeomorphism      81
Induced mapping      82
Induced orientation      93
Induced topology      53
Inner point      53 72
Integral module      231
Integral module, basis      231
Integral module, initial      231
Intersection      41 42
Interval, closed      48
Interval, half-open      49
Interval, open      48
Inverse image      43
Inverse mapping      43
Isomorphic complexes      80
Isomorphism      80 219
Jordan theorem      182
Jordan — Brouwer theorem      182
Kernel      220
Klein bottle      38
Kronecker delta      68 223
Lebesgue number      64
Lebesgue’s lemma      64
Lefschetz duality theorem      179
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