Whyburn G.T. — American mathematical society colloquium publications. Volume XXVIII :: Электронная библиотека попечительского совета мехмата МГУ

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Whyburn G.T. — American mathematical society colloquium publications. Volume XXVIII

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Название: American mathematical society colloquium publications. Volume XXVIII

Автор: Whyburn G.T.

Аннотация:

The material here presented represents an elaboration on my Colloquium Lectures delivered before the American Mathematical Society at its September, 1940 meeting at Dartmouth College. The results of some of my own efforts together with a selection of those of other mathematicians relative to the subject chosen are presented in what is intended to be a coherent and approximately self-contained exposition, framed in the familiar topology of separable metric spaces. No attempt is made at comprehensive coverage either of the known work embraced by the title of the book or of the work of others, or even myself, which may be closely related to that included.

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Рубрика: Математика/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 1942

Количество страниц: 290

Добавлена в каталог: 12.03.2015

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Предметный указатель

$E_{0}$ -set      64
$G_{\delta}$ -set      28
$G_{\delta}$ -sets      28
$Q_{\omega}$ , $Q^{'}_{\omega}$       6
$V_{\epsilon}(X)$       12
$\epsilon$ -chain      13
$\epsilon$ -set      31
$\theta$ -curve (Theta-curve)      104
$\theta$ -curve (Theta-curve), separation of plane by      104
A-set      67 ff.
A-set, invariance of      145
A-set, true A-set      68
Absolute neighborhood retract      216
Accessibility      111
Accessibility from all sides      111
Accessibility, regular      111
Acyclic curve      88
Additive system      97
ARC      36
Arc wise connectedness      36
Arc-curve      80
Bibliography      266
Borel set      52
Borel set, classification of cut points      52
Borel theorem      5
Boundary      16
Boundary of an open set      16
Boundary, curve      76 165
Boundary, elements of a plane region      160
Brouwer fixed point theorem      243
Brouwer Reduction Theorem      17
Cactoid      76
Cactoid, invariance under monotone mappings      171
Cantor discontinuum      35
Cantorian manifold (local)      149
cell      116
Cell, 2-cell, characterization of      119
Characteristic, Euler      201
Characterization of the sphere      114
Closure of a set      2
Collection      1
Collection, countable      1
Collection, null      67 134
Collection, semi-closed      131
Collection, upper semi-continuous      122
Compact set      3
Complete enclosure      27
Complete space      27
Complete, locally      158
Component      13
Component, orbit      259
Conditionally compact set      5
Conjugate points      64
Connected set      13
Continua      15
Continua of convergence      18 70 81
Continua, E-continua      112
Continua, generalized      16
Continua, hereditarily locally connected      89 ff.
Continua, irreducible      17
Continua, n-dimensional      96 ff.
Convergence of sequence of sets      10
Convergence of sequences of points      3
Convergence, 0-regular      174
Covering theorems      4
Curve, acyclic      88
Curve, boundary      76 165
Curve, classification      98
Curve, rational      82—83 96
Curve, regular      82—83 96
Curve, simple closed      57
Cut point, cutting      41
Cut point-order theorem      49 ff.
Cyclic chain      71
Cyclic chain, approximation theorem      73
Cyclic chain, development      73 ff.
Cyclic connectedness      77 ff.
Cyclic connectedness, theorem      79
Cyclic element      66
Cyclic element, invariance      241 ff.
Cyclic set      107
Cyclic, additivity of b(X)      234
Cyclic, additivity of r(X)      85
Cyclidy extensible and cyclicly reducible properties      81 ff.
Decomposition space      123
Decomposition, upper semi-continuous      123
Degree of a transformation      199
Degree of multi coherence      83
Dendrite      88
Diameter      9
Dimensionality      82—83 96
Disjoint sets      1
Distance      9
Divisibility theorem      49
E-continuum      112
End point      64
Equicontinuous powers of a transformation      252
Equicontinuous powers of a transformation, relation to regular almost periodicity      252
Equivalence of two transformations      127
Equivalence to 1      220 ff.
Equivalence to 1 on cartesian product spaces      223
Equivalence to 1, cyclic extensibility of      222
Essential transformation      225
Euler characteristic      201
Euler characteristic, effect of interior transformation on      202 208
Exponential equivalence      225
Extension of transformations      28 179
Extension of transformations, interior      213 215
Extension of transformations, monotone, of non-alternating      180
Factor Theorem      141
Factorization      134 141
Factorization, monotone-light      143
Fixed point      240
Fixed point, property      242
Fixed point, theorem (Brouwer)      243
Frontier, F(G)      16
Generalized continuum      16
Graph (linear)      182
Graph (linear), interior transformations on      182
Groups $S^{X}$ , P, B(X)      229 ff.
H-set      72
Hemi-cactoid      172
Hemi-cactoid, invariance under monotone transformations      173
Hereditarily locally connected continua      89 ff.
Hereditarily locally connected continua, invariance under monotone mapping      138
Hereditarily locally connected continua, rationality of      93 ff.
Hereditary system      97
Hilbert parallelotope      6
Hilbert space      6
Homeomorphism      24
Homeomorphism of original and image sets      135
Homeomorphism, local      199
Homotopy      225 ff.
Hyperspace (of upper semi-continuous decomposition)      123
Imbedding theorems      33 74
Inducible property      17
Interior transformations      129
Interior transformations on dendrites      185
Interior transformations on inverse sets      147
Interior transformations on pseudo-manifolds      205
Interior transformations on simple arcs      184
Interior transformations on simple closed curves      184
Interior transformations, action on linear graphs      182
Interior transformations, analysis in the large of      200
Interior transformations, analysis in the small of      198
Interior transformations, effect on the numbers b(X) and $\rho(X)$       232
Interior transformations, finite-to-one property      189
Interior transformations, invariance of 2-manifolds      191 ff.
Interior transformations, invariance of boundary curves      185
Interior transformations, invariance of nodal set      148

Interior transformations, inversion of arcs and dendrites      186
Interior transformations, inversion of components      148
Interior transformations, inversion of cyclic elements      151
Interior transformations, inversion of quasi-components      147
Interior transformations, non-increasing of order      147
Interiority at a point      149
Invariant, cyclic elements      242 248
Invariant, point      240
Invariant, set      240
Invariant, set (completely)      253
Inverse set      137
Irreducible continuum      17
Irreducible cutting      43
Irreducible transformations      162 ff.
Joining of sets by regions      93
Jordan curve theorem      100 ff.
Limit, point      2
Limit, superior and inferior      10
Limit, theorem      14
Lindeloef theorem      4
Local homeomorphism      199
Local separating point      61
Locally compact set      15
Locally connected continua      23 ff.
Locally connected continua, equality of r(X) and $\rho(X)$ for      238
Locally connected set      18 20
Locally connected set, inversion under interior transformations      189
Locally connected set, uniformly      22
Manifold, 2-dimensional      193
Manifold, cantorian      149
Manifold, invariance under interior transformations      191 ff.
Manifold, pointwise periodic mappings on      262
Mapping of 2-cell onto arbitrary hemi-cactoid      177
Mapping of boundary elements of a plane region      160
Mapping of circle onto arbitrary boundary curve      166
Mapping of cyclic elements and A-sets      144
Mapping of interval onto arbitrary locally connected continuum      33
Mapping of plane region onto circle interior      161
Mapping of sphere onto arbitrary cactoid      175
Mapping onto the circle      219 ff.
Mapping, interior non-alternating, onto interval and circle      218
Mapping, monotone, of locally connected continuum into regular curve      219
Mapping, theorems      33 ff.
Metrization theorem      7
Monotone transformations      70 127
Monotone transformations of local connected continua into regular curves      219
Monotone transformations on spheres, cactoids, planes, and 2-cells      170 ff.
Monotone transformations, characterizations of      137 ff.
Monotone transformations, effect on the numbers b(X) and $\rho(X)$       232
Multicoherence, degree of      83
Multicoherence, degree of, cyclic additivity of      85
Mutually separated sets      13
Nodal set      77 148
Node      77
Non-alternating transformations      127
Non-alternating transformations on boundary curves      165 ff.
Non-alternating transformations, characterizations of      137 ff.
Non-cut point existence theorem      54
Non-separated collection      42
Non-separated cuttings      44 ff.
Null sequence (collection or family)      67 134
Orbit      253
Orbit, component      259
Orbit, continuity of      257 ff.
Orbit, decomposition      253 ff.
Orbit, invariance under limit taking      259
Orbit, potential      45
Order of a subset      48
Ordered set      41
Ordered set, naturally      41
Perfect set      53
Periodic transformation      239
Periodic transformation, almost      246
Periodic transformation, elementwise      248
Periodic transformation, pointwise      239
Periodic transformation, pointwise almost      246
Periodic transformation, reduction of pointwise periodic to periodic on manifolds      262 ff.
Periodic transformation, reduction of pointwise periodic to regularly almost periodic      262
Periodic transformation, regular almost      250
periodicity      239 ff.
Periodicity, almost      246
Periodicity, regular almost      250
Phragmen — Brouwer Theorem      105
Plane separation theorem      108
Point      1
Point of sets      1
Point, condensation      4
Point, fixed      240
Point, limit      2
Point, theorems for transformations      140
Points of interiority of a transformation      149
Product, cartesian or topological      6
Property S      20 111
Pseudo-manifold      205
Pseudo-manifold, interior transformation on      205
Quasi-component      90
Quasi-monotone transformation      151
Quasi-monotone transformation, characterizations of      152—153
Quasi-monotone transformation, effect on degree of multicoherence      153
Quasi-monotone transformation, invariance under      153—154
Rational curve      82—83 96 138
Reduction Theorem      17
Region      20
Regions and their boundaries      111 ff. 158
Regular chain      36
Regular convergence      174
Regular curve      82—83 96 138
Regular set      19
Regular space      2
Relative distance transformation      154
Retract, absolute neighborhood      216 ff.
Retractions      70 143
Retractions, non-alternating interior, of locally connected continua into arcs      212
Retractions, non-alternating interior, of locally connected continua into simple closed curves      213
Saturated collection      45
Semi-closed (set, collection)      131 ff.
Semi-locally-connected set      19
Separability      3
Separating point      58
Separating point, order theorem      60
Separation      13
SEQUENCE      1
Sequence, convergence of      3 10
Sequence, null      67
Sets, compact      3
Sets, countable      1
Sets, dense      30
Sets, locally compact      15
Sets, locally connected      18
Sets, nondegenerate      30
Sets, open and closed      3
Sets, operations with      1
Sets, perfect      53
Sets, regular      19
Sets, semi-closed      131
Sets, semi-locally-connected      19
Sets, totally disconnected      34
Simple arcs, interior transformations on      184
Simple arcs, pointwise periodic mappings on      264
Simple arcs, properties of      54 ff.
Simple closed curves      57
Simple closed curves, interior transformation on      184
Simple closed curves, pointwise periodic mappings on      264
Simple closed curves, separation of plane or sphere by      100 ff.
Simple link      64
Space of continuous mappings      27
Space, complete      27
Space, Hilbert      6
Space, metric      5
Space, normal      6

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