Morris S.A. — Topology without tears :: Электронная библиотека попечительского совета мехмата МГУ

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Morris S.A. — Topology without tears

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Название: Topology without tears

Автор: Morris S.A.

Язык:

Рубрика: Математика/Геометрия и топология/Общая топология/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2003

Количество страниц: 211

Добавлена в каталог: 20.04.2005

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Предметный указатель

      103
$f^{-1}$       17
$F_{\sigma}$ -set      28 127
$G_{\delta}$ -set      28 127
      103
      103
$L_{\infty}$       103
-space      20
-space      20 147
-space      62 100
-space      62
-space      104
$\mathbb{N}$       3 60
$\mathbb{P}$       28 60
$\mathbb{Q}$       27 60
$\mathbb{R}$       8 24 159
$\mathbb{R}^2$       33
$\mathbb{R}^n$       33
$\mathbb{S}^1$       154
$\mathbb{S}^n$       154
$\mathbb{T}$       159
$\mathbb{Z}$       27 60
$\mathcal{P}(S)$       172
$\mathfrak{N}_0$       165
0-dimensional      89
Accumulation point      45
Algebraic number      169
Analytic set      115
arrow      77
Axiom, least upper bound      54
Baire category theorem      123
Baire space      124
Ball, closed unit      141
Banach space      118
Banach, Fixed Point Theorem      121
Basis      30
Bijection      164
Bijective      16
Bikompakt      142
Bolzano — Weierstrass theorem      112
Bound greatest lower      54
Bound lower      54
Bound upper      54
Bounded      54 137
Bounded above      54
Bounded below      54
Brouwer fixed point theorem      87
C      177
Cantor, Georg      172
Card      177
cardinal number      177
Cardinality      165
Category, first      125
Category, second      125
Cauchy sequence      109
Circle group      159
Clopen, set      12
Closed mapping      140 148
Closed set      10
Closed unit ball      141
Closure      47
Cluster point      45
Coarser topology      84 148
Cofinite topology      14
Compact      131 132
Compact space      132
Compactum      158
complete      110
Completely metrizable      114
Completion of a metric space      116
Component      88 156 157
Connected      55
Connected, component      156
Connected, locally      159
Connected, path      85
Connected, pathwise      85
continuous      77
Continuous mapping      79
Continuum      157
Contraction mapping theorem      121
Contraction, mapping      120
Contradiction      26
Converge      105
Converse of Heine — Borel Theorem      137
Convex, set      125
Countability, first axiom of      104
Countability, second axiom of      35
Countable bases      104
Countable closed topology      20
Countable set      165
Countably infinite      165
Covering, open      132
Cylinder      155
C[0, 1]      41 141
Decreasing sequence      111
Dense      48
Dense, everywhere      48
Dense, nowhere      123
Denumerable      165
Diagonal      146
Dimension, zero      89
Disconnected      56 85
Disconnected, totally      88
Discrete metric      92
Discrete space      3
Discrete topology      3
Distance      91
Distance between sets      109
Element, greatest      54
Element, least      54
Embedding, isometric      116
Empty union      7
Equipotent      164
Equivalence relation      76 117 164
Equivalent metric      99
Euclidean metric      92
Euclidean metric on $\mathbb{R}^2$       92
Euclidean topology      24
Euclidean topology on $\mathbb{R}^n$       33
Everywhere dense      48
Final segment topology      8
Finer topology      84 148
finite      165
Finite subcovering      132
Finite-closed topology      14
First axiom of countability      104
First category      125
First countable      104
Fixed point      87 120
Fixed point property      87
Fixed point theorem      87
Fixed Point Theorem, Banach      121
Function, bijective      16
Function, continuous      77
Function, injective      16
Function, inverse      16
Function, one-to-one      16
Function, onto      16
Function, surjective      16
Fundamental theorem of algebra      160
Generalized Heine — Borel Theorem      138 154
Georg Cantor      172
Greatest element      54
Greatest lower bound      54
Group of homeomorphisms      69
Group, circle      159
Group, topological      159
Hausdorff space      62 100 146
Heine — Borel theorem      137
Heine — Borel Theorem, Converse      137

Heine — Borel Theorem, Generalized      138
Homeomorphic      63
Homeomorphism      63
If and only if      29
Image, inverse      17
Increasing sequence      111
Indiscrete, space      3
Indiscrete, topology      3
Induced topological space      98
Induced topology      58 98
Infimum      54
Infinite      165
Infinite, countably      165
Initial segment topology      8
Injective      16
int      53 123
Interior      53 123
Intermediate Value Theorem      86
Intersection of topologies      21
interval      72
Inverse, function      16
Inverse, image      17
Isolated point      127
Isometric      104 116
Isometric, embedding      116
Isometry      104 116
Least element      54
Least Upper Bound Axiom      54
Limit point      45
Line, Sorgenfrey      54 134 147
Locally compact      155
Locally connected      159
Lower bound      54
Lower semicontinuous      128
Map, bijective      16
Map, injective      16
Map, inverse      16
Map, one-to-one      16
Map, onto      16
Map, surjective      16
Mapping, closed      140 148
Mapping, continuous      79
Mapping, contraction      120
Mapping, lower semicontinuous      128
Mapping, open      140 148
Mapping, upper semicontinuous      128
Mathematical proof      2
Meager      125
Mean value theorem      122
Metric      91
Metric space, complete      110
Metric, discrete      92
Metric, equivalent      99
Metric, Euclidean      92 92
Metric, space      91
Metrizable      101
Metrizable, completely      114
Monotonic sequence      111
n-sphere      154
Neighbourhood      50
Norm      95
Normal space      104 141
Normed vector space      95
Nowhere dense      123
Number, algebraic      169
Number, cardinal      177
Number, transcendental      169
Object      77
One-to-one      16
One-to-one correspondence      164
Onto      16
Open ball      96
Open covering      132
Open mapping      140 148
Open mapping theorem      126
Open set      9
Path      85
Path-connected      85
Pathwise connected      85
Peak point      111
Point      45
Point, accumulation      45
Point, cluster      45
Point, fixed      87 120
Point, isolated      127
Point, limit      45
Point, neighbourhood of      50
Point, peak      111
Polish space      115
PRODUCT      144
Product of cardinal numbers      182
Product topology      35
Product, space      144
Product, topology      144 150
Proof, by contradiction      26
Proof, if and only if      29
Proof, mathematical      2
Proper subset      13
Property, fixed point      87
Property, separation      22
Property, topological      76
Reflexive      65
Regular      147
Regular space      62
Relation, equivalence      76 117 164
Relation, reflexive      65
Relation, symmetric      65
Relation, transitive      65
Relative topology      58
Second axiom of countability      35
Second axion of countability      147
Second category      125
Semicontinuous, lower      128
Semicontinuous, upper      128
Separable      52 115
Separation property      22
Sequence, Cauchy      109
Sequence, convergent      105
Sequence, decreasing      111
Sequence, increasing      111
Sequence, monotonic      111
Set, $F_{\sigma}$       28 127
Set, $G_{\delta}$       28 127
Set, analytic      115
Set, clopen      12
Set, closed      10
Set, convex      125
Set, countable      165
Set, denumerable      165
Set, finite      165
Set, first category      125
Set, infinite      165
Set, meager      125
Set, of continuous real-valued functions      64
Set, of integers      27 60
Set, of irrational numbers      28 60
Set, of natural numbers      3 60
Set, of positive integers      3 60
Set, of rational numbers      27 60
Set, open      9
Set, power      172
Set, second category      125
Set, uncountable      165
Sierpinski space      20
Sorgenfrey line      54 134
Souslin space      115
Space,       20
Space,       20 147
Space,       62 100
Space,       62

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