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| Janich K. — Topology |
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| Предметный указатель |
 88 see
 43
 66
 149
 -ball 8
 56
 -space 56
 45
 "hat" 51
 8
 75
 76
 66
+,"plus" 10
Accumulation point 3 see
Attaching 43
Attaching map 43
Axiom of Choice 171
Banach space 26
Basepoint 141
Basis 12
Bordant 76
Bordism classes 76
Boundary point 6
Branched covering 131
Brower, L. E. J., 1881-1966 94
C(X) 29 79
Cantor, Georg, 1845-1918 3 4 174 175
Cardinality 173
Category 66
cell 93
Cell decomposition 93
Chain 172
Characteristic map 95
Characteristic subgroup of a covering space 142
Choice, axiom of 171
Classification of covering spaces 144 149
Classification of covering spaces and the existence theorem on page 149
Classification of covering spaces, consists of the uniqueness theorem on page 144
Clifford — Klein forms 158 see
Closed 5
Closure 6
Closure finiteness 95
Cluster point 3
Coarse 12 see
Collapsing of a subspace 40
Commutative Banach algebra 164
Compact 18
Complete metric space 50
Complete topological vector space 28
Completely regular 166
Completion 51
Cone 40
Connected 14
Connected sum of two manifolds 45
Continuous map 12
Continuum Hypothesis 175
Contractible 61
Contravariant 69
Convergence 17
Convex property 120
Countability axioms 79
Covariant 69
Covering space 130
Covering transformations 149
cube 75 161
CW-complex 95
CX 40
D 8
Deck transformations 149 see
Deformation retract 62
Dense 51
Differential operators 57
Difftop 67
Discrete topology 12
Disjoint union 10
Distance 109
Dual 163
Euler characteristic, Euler number 71 72 104
Excursus on vector bundles 116
Existence theorem for covering spaces 149
Exterior point 6
Filter 169
Filter convergence 169
Fine 12
First countable 79 see
Forgetful functor 70 92
Fourier series 3
Frechet space 28
Frechet, Maurice, 1878-1973 3 24 27
functor 69
Fundamental group 141
G-space 37
G/H 34
Gelfand' — Neumark representation for B*-algebras 166
GENERATED 12
Grassmannian manifold 36
Handle 44
Hausdorff separation axiom 17
Hausdorff space 17
Hausdorff, Felix, 1868-1942 2
Hilbert basis 26
Hilbert cube 162
Hilbert space 26
Homeomorphic 13
Homeomorphism 13
Homogeneous space 35
Homology 72 73 103
Homotopic 59
Homotopy 59
Homotopy category 68
Homotopy classes 61
Homotopy equivalence 61
Homotopy groups 75
Homotopy inverse 61
Ideal limit points 52
Incidence data 91
Incidence numbers 103
Induced topology 10
Induction principle 172
Interior 6
Interior point 6
Invariant 70
Isomorphism 129
Isomorphisms 68
| Isotropy group 39 see
Klein bottle 46
Kuratowski closure axioms 7
Leaves, number of 130 see
lexicographical ordering 172
Lie groups 85 159
Liftability criterion 142
Locally convex 28
Locally homeomorphic 130
Locally path connected 142
Locally trivial fibration 129
Manifold 19 85 106
Metric space 8
Metrizable space 9
Mobius strip 46
Monodromy lemma 136
Mor(X,Y) 66
Morse theory 44
Neighborhood 5
Neighborhood axioms 7
Neighborhood basis 78
Norm 26
Normal covering space 151
normalizer 151
North pole 42
Null-homotopic 147
Number of leaves 130
open 5
Open ball 8
Open boxes 11
Open cover 18
Orbit 37
Orbit space 38
Ordinals 174
P(X) 7 174
Paracompact 124
Partially ordered set 171
Partition 93
Partition of unity 116
Path 15
Path lifting 133
Path-connected 15
Peano, Giuseppe, 1858-1932 152
Polyhedron 88 see
Pre-Frechet space 28
Product of topological spaces 11 80
Product topology 11
Quasi-compact 18
Quotient space 31
Quotient topology 31
Recursion formula 172
Recursive definition 172
Reflexive Banach space 163
Retract, retraction 62
Riemann metric 122
Riemann surfaces 157
Riemann, Bernhard, 1826-1866 3 122 157
Schroder — Bernstein theorem 173
Second countable 79 see
Section 73 117
Semi-local simply connected 148
Semmorm 27
Separable 85
Sequentially compact 83
Sequentially continuous 82
Shrinking 126
simplex 88
Simplicial category 92
Simplicial complex 88
Simplicial homology 92
Simplicial map 92
Simply connected 148 152
Skeleton 96
Small category 69
Smash product 42
Sobolev space 58
Solid torus 63
Space forms 158
Space-filling curve 152
Spectrum 165
Stabilizer 39
Stone-Cech compactification 166
Subbasis 12
Subcomplex 98
Subordinate 116
Subsimplex 88
Subspacc 10
Subspace topology 10 see
SUM 10
Support 107
Suspension 41
Thorn space 42
Tietze extension lemma 114
TM 117
Top 66
Topological group 25 34
Topological space 5
Topological space over X 128
Topological sum 10 see
Topological vector space 24
topology 5
Topology of a metric space 8
Transitive 151
Triangle inequality 8
Trivial topology 12
Tychonoff product theorem 160
Tychonoff, Andrej Nikolajevitch, 1906 160
Ultrafiltcr 169
Uniformly continuous 55
Uniqueness theorem for covering spaces 144
Universal cover 152
Urysohn lemma 109
Urysohn, Pavel Samuilovitch, 1898-1924 109
Vector bundle 117
Vector field 19
Weak topology 30 81 95 101 163
Wedge product 42
Well-ordered 172
Whitehead, J. H. C, 1904-1960 96
Winding number 75
X/A 40
X/G 38
X/~ 31
Zariski topology 17
Zorn's lemma 172
[X,Y] 61
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