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Seebach J.A., Steen L.A. — Counterexamples in Topology
Seebach J.A., Steen L.A. — Counterexamples in Topology

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Название: Counterexamples in Topology

Авторы: Seebach J.A., Steen L.A.

Аннотация:

This compendium contains significant examples of topological spaces, each analyzed in detail. Numbering almost 150, the examples range from the familiar to the obscure and are preceded by a succinct exposition of general topology and basic terminology and theory. Oveer 25 Venn diagrams and reference charts summarize the examples` properties and allow the reader to scan quickly for examples with prescribed properties.


Язык: en

Рубрика: Математика/Геометрия и топология/Общая топология/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1970

Количество страниц: 210

Добавлена в каталог: 20.11.2004

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$F_\sigma-$set      3
$G_\delta-$set      4
$T_4$ fully      23
$T_4$ perfectly      16
$T_i$ space      11
$\epsilon-$net      36
$\omega-$acumulation point      5
$\sigma-$compact      19
$\sigma-$locally compact      21
$\sigma-$locally finite base      37
Accumulation point, $\omega-$      5
Accumulation point, of a sequence      5
Adherent point      5
Alexander's compactness theorem      18
Alexandroff plank      107
Alexandroff square      120
Appert space      117
ARC      29
Arc component      29
Arc connected      29
Arens square      98
Arens — Fort space      54
Baire category theorem      25 37 197
Baire metric      123 124
Ball (open)      34
Base $\sigma-$locally finite      37
Base of a filter      9
Base of a topogy      4
Base symmetric (for a quasiuniformity)      38
Basis      4
Basis equivalent      4
Basis local      4
Bernstein's connected sets      142
Biconnected      33
Bijoctive function      8
Bing's space      157
Boundary      6
Bounded      36
Bounded totally      36
Cantor set      57
Category first      7
Category second      7
Cauchy      154
Cauchy completion      154
Cauchy sequence      36
Closed extension topology      44
Closed function      8
Closed set      3
Closure      6
Cluster point      10
Coarser filter      10
Cofinite topology      49
Compact      4 18
Compact $\sigma-$      19
Compact $\sigma-$locally      21
Compact countably      19
Compact locally      20
Compact meta-      23
Compact para-      23
Compact pre-      36
Compact pseudo-      20
Compact sequentially      19
Compact strongly locally      20
Compact weakly countably      19
Compactification, one point      63
Compactification, Stone — Cech      129
Comparable filters      10
Comparable topologies      3
Compatible uniformities      38
complete      36
Complete order      67
Complete topologically      37
Completely Hausdorff      13
Completely normal      12
Completely regular      14
Completely separable      7
Completion      37
Component      28
Component, arc      29
Component, path      29
Component, quasi-      29
Composant      33
Condensation point      5
Connected between two points      29
Connected hyper-      29
Connected in kleinen      200
Connected in X      28
Connected locally      30
Connected path      29
Connected set      7 28
Connected space      28
Connected strongly      198
Connected ultra-      29
Connected, arc      29
Connected, locally arc      30
Connected, locally path      30
Continua      33
Continuous at a point      8
Continuous function      7
Continuum Hypothesis      50 197
Convergence of a filter      10
Convergence of a sequence      5
Countable chain condition      22
Countable first      7 22
Countable second      7 22
Countably compact      19
Countably metacompact      23
Countably paracompact      23
Courser topology      3
Cover, open      4
Cover, refinement of      22
Cube, Hilbert      65
Cut point      33
Cylinders, open      8
Degenerate      28
Dense set      7
Dense-in-itself      6
Derived set      5
Diagonal      38
Diameter      36
Dieudonne plank      108
Disconnected, extremally      32
Disconnected, totally      31
Disconnected, totally pathwise      31
Discrete metric      41
Discrete topology      41
Discrete uniformity      42
Dispersion point      33
Distance      34
Double pointing      51 191
Duncan's space      153
Entourage      38
Entourage symmetric      38
Equivalent bases      4
Equivalent subbasis      4
Equivalent, topologically      8
Euclidean topology      56
expansion      15
Exterior      7
Extremally disconnected      32
Filter      9
Filter base      9
Filter base, limit of      10
Filter coarser      10
Filter comparable      10
Filter finer      9
Filter neighborhood      10
Filter strictly coarser      10
Filter strictly finer      10
Filter, convergence of      10
Filter, limit point of      10
Filtered by      9
Filtered set      9
Finer filter      9
Finer topology      3
Finite complement topology      49
Finite intersection axiom      18
Finite intersection property      9
First category      7
First countable      7 22
Fixed ultrafilter      10
Fort space      52
Frechet product metric      64 152
Frechet space      11 64
Free ultrafilter      10
Frontier      6
Fully $T_4$      23
Fully normal      23
Function closed      8
Function continuous      7
Function open      8
Function Urysohn      13
Function, bijective      8
Gustin's space      142
Half-open interval topology      75
Half-open square topology      103
Hausdorff space      11
Hausdorff space completely      13
Hausdorff's metric      154
Helly space      127
Hereditary      4
Hereditary, weakly      4
Hewitt's condensed corkscrew      111
Hilbert cube      65
Hilbert space      64
Homeomorphic      8
Homeomorphism      8
Hyperconnected      29
Identification topology      9
Indecomposable      33
Indiscrete topology      42
Induced topology      4
Interior      6
Interval topology      66
Invariant, topological      8
Irrational numbers      59
Irreducible subcovering      23
Isolated point      6
Isometric      37
Kolmogorov space      11
Larger topology      3
Lexicographic order      73
Limit point      5
Limit point of a filter      10
Limit point of a filter base      10
Limit point of a sequence      5
Lindeloef      19
Local basis      4
Locally arc connected      30
Locally compact      20
Locally connected      30
Locally finite refinement      22
Locally path connected      30
Long line      71
Lower limit topology      75
Meager      7
Metacompact      23
Metacompact countably      23
Metric      34
Metric Baire      123 124
Metric discrete      41
Metric Frechet      64 152
Metric Hausdorff      154
Metric product      64 152
Metric Sierpinski      152
Metric space      34
Metrizable, quasiumform space      38
Metrizable, topological space      37
Michael's subspace      157
Michael's topology      105
Miller's set      148
Neighborhood      4
Neighborhood filter      10
Neighborhood, open      4
Nested sequence of sets      37
Net, $\epsilon-$      36
Niemytzki's topology      100
Nonprincipal ultrafilter      10
normal      12
Normal completely      12
Normal fully      23
Normal perfectly      16
notes      189
Novak space      134
Nowhere dense set      7
Numbers, irrational      59
Numbers,rational      59
One point compactification      63
Open ball      34
Open cover      4
Open cylinder      8
Open extension topology      47
Open function      8
Open neighborhood      4
Open set      3
Order topology      66
Ordinal space      68
p-adic topology      81
Para compact      23
Para compact count ably      23
Para compact pointwise      23
Particular point topology      44
Path      29
Path component      29
Path connected      29
Perfect set      6
Perfectly $T_4$      16
Perfectly normal      16
Perfectly separable      7
Plank, Alexandroff      107
Plank, Dieudonne      108
Plank, Thomas'      113
Point finite refinement      22
Point, $\omega-$accumulation      5
Point, adherent      5
Point, cluster      10
Point, condensation      5
Point, cut      33
Point, dispersion      33
Point, isolated      6
Point, limit      5
Pointwise paracompact      23
Precompact      36
Principal ultrafilter      10
Problems      181
Product invariance properties      26
Product metric      64 152
Product space      8
Pseudo-arc      147
Pseudocompact      20
Pseudometric      34
Pseudometrizable (quasiuniform space)      38
Punctiform      33
Quasicomponent      29
Quasimetrie      34
Quasiuniform space      38
Quasiuniformity      37
Quasiuniformity, separated      38
Quasiuniformizable      38
Quotient space      9
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