Shick P.L. — Topology: Point-set and geometric :: Электронная библиотека попечительского совета мехмата МГУ

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Shick P.L. — Topology: Point-set and geometric

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Название: Topology: Point-set and geometric

Автор: Shick P.L.

Аннотация:

Topology: Point-Set and Geometric presents an introduction to topology that begins with the axiomatic definition of a topology on a set, rather than starting with metric spaces or the topology of subsets of Rn. This approach includes many more examples, allowing students to develop more sophisticated intuition and enabling them to learn how to write precise proofs in a brand-new context, which is an invaluable experience for math majors. Along with the standard point-set topology topics—connected and path-connected spaces, compact spaces, separation axioms, and metric spaces—Topology covers the construction of spaces from other spaces, including products and quotient spaces. This innovative text culminates with topics from geometric and algebraic topology (the Classification Theorem for Surfaces and the fundamental group), which provide instructors with the opportunity to choose which "capstone" best suits his or her students...

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2007

Количество страниц: 277

Добавлена в каталог: 22.12.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$T_{0}$       144 148
$T_{1}$       144 148
$T_{2}$       144 148
$T_{3}$       149 152
$T_{4}$       150 153
$\coprod$       82
$\epsilon$ -ball      73—74 91 159
$\epsilon$ -diamond      74
$\epsilon$ -square      74
$\tau - \nu$ continuous      65
$\tau$ -closed      58
$\tau$ -open set      52
:=      47 57
Abbott, E.      170
Abel      39
Abel, N.      3
Abelian      2—3 41
Accumulation point      78
Ambient Space      105
Analysis situs      220
Antipodal      239
Associative      9
Axiom of Choice      31 34—35
Base space      237
Basepoint      92 218 232 235 244
Bases      74
Basis      154
Basis for topology on      72
Basis set      72 90
Behold!      28
Big Theorem on Maps into Products      93 99
Bijection      16
Boas, R.      9
Bolzano — Weierstrass theorem      163
Boundary      71 81—82
Boundary point      81
Bourbaki, N.      9
Box topology      99
Boy's Surface      183
Brouwer      251
Brouwer fixed point theorem      253
Brouwer, L.E.J.      219
Browder, B.      183
Calc-continuous      64
Calculus      64
Cantor's theorem      37
Cantor, G.      34
cardinal number      30
Cardinal numbers      36
cartesian      88
Cartesian product      11 97
Category      217
Cayley      40
Classification Theorem      191 195 210
Classification Theorem, finite simple groups      6
Closed      58 152
Closed graph theorem      147
Closure      59 79
Cluster point      78
Coarser      53 155
COBE      172
Cohen, P.      37
Cohen, R.      182
Combinatorial      202
Commutative      9
Compact and Hausdorff      154—155
Complement      8
composition      16 67
Concatenate      223
Concatenation      43 225
Conjugation      50
Connected sum      186—187 192 213
Constant path      225
Continuity      67
continuous      65 83
Continuous function      64
Continuum      36
Continuum Hypothesis      37
Contractible      221 224
Converge      166
Convergence      166
CONVERSE      54 155
Convex      233
Conway, J.      199
Coordinate set      100
Coset      25 49
Cosmic microwave background radiation      172
Countable      32
Countably infinite      32 34
Covering map      237
Covering space      237 260
Cyclic      247
Cylinder      5 180 185
DeMorgan's laws      11—12
Dense      61 148
Derived set      78
Dihedral group      44
Discrete      148 150
Discrete metric      159 162
Discrete space      53
Discrete topology      53
Disjoint union      82
Distance      157
Distinguished point topology      56 83 149 154
Distribute      9
Domain      15
Double inclusion proof      9
EDGE      196
Edges      196
Embedded      181
Embedding      181
Epimorphism      16
EQUIVALENCE      68 223
Equivalence class      24 101
Equivalence relation      24 30 101
Erlangen      39
Euclidean      1 3 8 51 157 158 170 171 175 179
Euclidean geometry      8
Euclidean metric      158
Euclidean transformation      2
Euler      39
Euler characteristic      210—211 213
Euler, L.      210
Exponential map      103
Extension      18
Exterior      83
Factor group      25 49
Figure-eight      259
Finer      53
finite      152
Finite complement topology      56 145
Finite product      91 146
Flatland      170
Frechet      144
Function      14
functor      217 235
Fundamental group      210 217 231 247 255 259
Galois      39
Gauss      39
General linear group      42
Generalized Continuum Hypothesis      37
Generator      47
Genus      4
global      55
Godel, K.      37
Group      2 39
Groupoid      230
Half-open n-ball      178
Handle      194
Hausdorff      131

Hausdorff, F.      52 144 148 162
Heine — Borel theorem      163
Hereditary      151 164
Hirschorn, M.      28
Homeomorphic      68
Homeomorphism      1 3 67—69 109 111
Homology groups      196
Homology theory      210
Homomorphism      39 47 218
Homomorphism, group      2
Homotopic      219
Homotopy      219
Homotopy classes of maps      224
Homotopy equivalence      219—220
Homotopy group      231
Homotopy inverse      220
Homotory equivalence      219
Hubble telescope      173
Identically equal      220
Identity function      68
Image      15
Image of a subset      19
Immersed      181
Immersion      181
Immersion conjecture      182
inclusion      91
Inclusions      151
Indexed collection      12
Indexing set      97
Indiscrete      150
Indiscrete space      53
Indiscrete topology      53
Induction      26 32
Infinite Cartesian product      91 96
Injection      15
Integers      8
Interior      60 71 80
Interior point      60
Intersection      9
Intersection, indexed collection      12
Inverse image      20
Invertible      17
Irrational numbers      34
Isolated point      78
Isometry      161
Isomorphic      47 218
Isomorphism      47
Isomorphisms      2
Kernel      48
Kervaire invariant      183
Klein      5 171 180 182 185 192 194
Klein bottle      5
Klein, F.      2 5
Knot theory      174
Kolmolgorov, A.      144
Lambda-tuple      97
Left hand topology      55
Left ray topology      68
Levin, J.      173
Lifting      241—242
LIMIT      167
Limit point      71 78
local      84
Locally      55 72
Loop      230
Manifold      170 174
Manifold with boundary      179
Metric      157—158
Metric basis      160
Metric space      161—162
Metric spaces      157
Metric topology      161
Metrizable      164
Microwave anisotropy probe      172
Moebius      178
Moebius band      5 185
Moebius, A.F.      39
Monomorphism      15
Morphisms      217
n-sheeted covering      238 246
Natural      218
Natural numbers      8
Neighborhood      59 144
Noneuclidean      39
Nonmetrizable      164
Nonorientable      179 182
normal      150—152 162
Objects      217
One-to-one function      15
Onto function      16
Open function      68
Open set      52
Oreintability      4
Orientation-preserving      206
Orientation-reversing      204
Pasting lemma      105 223 225 245
Path      221
Path lifting property      241 243
Path-connected      224 233
Path-homotopy      221
Path-homotopy class      225
Path-homotopy classes      225
Path-Homotopy Lifting Property      241 246
Peano, G.      26
Planar curves      4
Planar diagram      178 189 192
Planar model      199
Poincare, H.      210 220 231
Pointed space      218
Power set      52
Product space      90 254
Product topology      89 97 99
Projection      91 93
Projection map      247
Projective plane      183 198 259
Projective planes      191
proof      199
Pseudo metric      158
Quintie      39
Quotient      146
Quotient space      103 107
Quotient topology      101—102
RANGE      15
Rational numbers      8
Real line      151
Reflexive      23 101 223
Regular      149 151—152 154
Relation      23 30
Restriction      18 67 87
Retraction      236
Riemann surface      240
Right ray topology      55
Right rays topology      145 150
Ruffini      39
Russell's paradox      10 30
Satelite      172
Separable      61
Separation axiom      143
Separation axioms      148
SEQUENCE      166
Sequences      96
Set      7
Set, difference      8
Set, finite      31—32
Set, infinite      30—31
Sets, equivalent      30
Simple groups      169
Simplices      196
Simply-connected      219 233 249
Slinky trick      193

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