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Kelley J., Namioka I. — Linear Topological Spaces
Kelley J., Namioka I. — Linear Topological Spaces

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Название: Linear Topological Spaces

Авторы: Kelley J., Namioka I.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1963

Количество страниц: 256

Добавлена в каталог: 31.03.2006

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\kappa$-space      81
Absolute value      230
Absolute, $G_{\delta}$      96
Absorb      90
Absorption Theorem      90
Adjoint transformation      204
Adjoint, of a linear topological space      119
Adjoint, of a pseudo-normed space      51
Admissible family      167
Admissible family, generated by $\mathcal{A}$      168
Algebra (of sets)      157
Algebraic, closure      42
Algebraic, dual      8
Annihilator      119
Approximation theorem      144
Ascoli theorem      81
atom      56
Baire, condition of      92
Baire, theorem      86
Banach — Alaoglu theorem      155
Banach — Steinhaus theorem      104
Banach, space      58
Banach, subgroup theorem      93
Barrel      104
Barrel, theorem      104
Base, for a family of pseudo-norms      232
Base, for a neighborhood system      27
Base, local      31
Base, local, theorem      34
Bilinear mapping      106
Bilinear, functional      106 137
Borel set      126
Bornivore      see "Bound absorbing"
Bound absorbing      182
Bounded      44
Bounded, elementary facts on boundedness      45
Bounded, linear function      45
Bounded, pointwise      103
Bounded, uniformly      102
Canonical, isomorphism      120
Canonical, map      137
Categorical imperative      1—247
Category, first      84
Category, first, at a point      85
Category, second      84
Category, second, at a point      85
Category, theorems      83
Circled      14
Circled extension      14
Closable map      208
Closed map      208
Closed set      27
Closed sphere      29
Closed, graph theorem      97 106 116
Closed, relation theorem      101
Closure      27
Cluster point      28
Co-base      113
Co-dimension      5
Complementary      5
complete      56
Complete metric space      32
Complete, relative to a pseudo-metric      85
Complete, sequentially      58
Complete, topologically      96
Completely continuous map      79 206
Completion      62
Condensation theorem      85
Cone      16
Cone, dual      225
Cone, generated by a set      17
Cone, generating      225
Cone, normal      227
Cone, positive      16
Cone, proper      19
Cone, reproducing      225
Conical extension      17
conjugate      see "Adjoint"
Contain small sets      59
Contraction      33
Converge      28
Convergence in mean of order p      54
Convex      13
Convex body      110
Convex cover      see "Convex extension"
Convex envelope      see "Convex extension"
Convex extension      13
Convex hull      see "Convex extension"
Coset space      see "Quotient space"
Deficiency      see "Co-dimension"
Dense      27
Difference, space      see "Quotient space"
Difference, theorem      92
DIMENSION      4
Direct (verb)      28
Direct, sum      8
Direct, system      see "Inductive system"
Disjoint elements (in a lattice)      230
Disk      see "Barrel"
Distinguish points      109 138
distribution      197
Dual, (of a linear topological space)      see "Adjoint"
Dual, base      see "Co-base"
Dual, ordering      225
Dual, transformation      199
Ecart      see "Pseudo-metric"
Elementary facts on totally bounded sets      65
Embedding      47
Equicontinuous      73
Equicontinuous, at a point      73
Euclidean, complex      3
Euclidean, real      3
Eventually      28
Exhaustible      see "Of the first category" "Category"
Extension theorem      21 117
Extreme, half-line      133
Extreme, point      130
Factor space      see "Quotient space"
Finite intersection property      59
Flat      see "Linear manifold"
Frechet space      58
Frequently      28
Function bounded on a set      69
Function, absolutely homogeneous      15
Function, additive      157
Function, analytic      162
Function, completely continuous      79 206
Function, continuous      28
Function, continuous, at a point      28
Function, continuous, on a subset      28 73
Function, interior      see "Open function"
Function, locally measurable      129
Function, lower semi-continuous      94
Function, non-negatively homogeneous      15
Function, open      28
Function, relatively open      28
Function, subadditive      15
Function, topological      see "Homeomorphism"
Function, totally bounded on a subset      70
Function, uniformly continuous      38
Function, upper semi-continuous      94
Function, vanishing at infinity      81
Function, weakly analytic      162
Generated by subspace      4
Graph      38
Grothendieck's Completeness Theorem      145
Hahn — Banach theorem      21
Half-space      19
Half-space, complementary      19
Hamel base      3
Hausdorff uniformity      116
Hausdorff's theorem on total boundedness      61
Helly's, condition      151
Helly's, theorem      18
Hilbert space      65
Hilbert space, orthogonal      66
Hilbert space, orthogonal complement      66
Hilbert space, orthonormal, basis      67
Hilbert space, orthonormal, subset      67
Hilbert space, projection      66
Hilbert space, summable      66
Homeomorphism      28
Hurewicz, W.      88
Hypercomplete      116
Hyperplane      19
Idempotent operator      40
Induced map theorem      6 40
Inductive limit      10
Inductive limit, strict      164
Inductive system      10
Inexhaustible      see "Of the second category" "Category"
Injection (into a direct sum)      9
Inner product      54
Interior      27
Inverse, limit      see "Projective limit"
Inverse, system      see "Projective system"
James, R.C.      198
Join (in a lattice)      229
Join (of two sets)      14
Kakutani's lemma      17
Kernel      see "Null space"
Kernel (of an inductive system)      10
Kothe space      220
Krein — Milman theorem      131
Krein — Smulian Theorem      177 212
L space      238
L space, characterization      243
Lattice, Archimedean      229
Lattice, Banach      236
Lattice, homomorphism      237
Lattice, homomorphism, real      237
Lattice, isomorphism      237
Lattice, normed      236
Lattice, normed, type L      238
Lattice, type L, representation      243
Lattice, type M      238
Lattice, type M, representation      240
Lattice, vector      229
LF space      218
LF space, generalized      218
LIMIT      28
Line segment      13
Linear topological space      34
Linear topological space, barrelled      104 171
Linear topological space, bornivore      see "Bound linear topological space"
Linear topological space, bound      183
Linear topological space, disk      see "Barrelled linear topological space"
Linear topological space, evaluable      192
Linear topological space, fully complete      178
Linear topological space, infra-tonnele      see "Evaluable linear topological space"
Linear topological space, locally bounded      55
Linear topological space, locally convex      45
Linear topological space, Mackey      173
Linear topological space, Montel      196
Linear topological space, normable      43
Linear topological space, pseudo-normable      44
Linear topological space, quasi-barrelled      see "Evaluable linear topological space"
Linear topological space, quasi-tonnele      see "Evaluable linear topological space"
Linear topological space, quotient      39
Linear topological space, reflexive      191
Linear topological space, semi-reflexive      189
Linear topological space, symmetric      see "Evaluable linear topological space"
Linear topological space, tonnele      see "Barrelled linear topological space"
Linear topological subspace      39
Linear, extension      5
Linear, function      5 see mapping transformation"
Linear, functional      6
Linear, hull      see "Linear extension"
Linear, invariant      6
Linear, isomorphism      see "A one-to-one linear function not 6
Linear, manifold      5
Linear, relation      101
Linear, space      1
Linear, span      see "Linear extension"
Linear, variety      5
Localizable measure space      129
Locally convex set      42
Locally convex topology      45
Locally convex topology, derived from $\mathscr{I}$      109
Locally convex topology, strongest      53
M space      238
M space, characterization      242
MAP      see "Function"
Mapping      see "Map"
Maximal linear subspace      7
Meager      see "Of the first category" "Category"
Measure      126
Measure, Borel      126
Measure, complex      126
Measure, regular      126
Measure, simple      186
Measure, Ulam      186
Meet      229
Metric      29
Metric, associated with a norm      43
Metric, Hausdorff      33
Metric, space      29
Metric, space, complete      32
Metric, topology      see "Topology"
Metrization theorem      48
Midpoint convex      17
Minkowski functional      15
Negative part      230
Net      28
Net, Cauchy      56
Net, Cauchy, relative to a pseudo-metric      57
Net, equicontinuous      73
Net, scalar      178
Net, universal      see "Kelley [5] p.
Norm      16
Norm, conjugate      117
Norm, equivalent      43
Norm, of a linear functional      117
Normed space      see "A linear space with a norm"
Nowhere dense      84
Null space      6
Open, (set)      27
Open, (set), $\mathscr{I}$-open      27
Open, (set), mapping theorem      99
Open, (set), sphere      29
Order, bounded set      228
Order, dual      225
Ordered linear space      225
Orthogonal      119
Osgood theorem      86
Paired spaces      137
Pairing      137
Pairing, induced      146
Pairing, natural      138
Pairing, separated      138
Partial ordering      16
Partial ordering, translation invariant      16
Partially ordered linear space      see "Ordered linear space"
polar      141
Polar, computation rule      141
Positive, cone      16 225
Positive, element      225
Positive, part      230
Precompact      see "Totally bounded"
Projection      8 40
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