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Robertson A.P., Robertson W. — Topological vector spaces

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Название: Topological vector spaces

Авторы: Robertson A.P., Robertson W.

Аннотация:

The aim of tbli tract is to give an account of the theory of topological vector spaces. There are many branches of functional analysis which depend upon this theory; it forms, for example, the background for the theory of distributions. In addition, it often clarinet results in the theory of normed spaces, especially those concerned with the weak topology, to regard them as particular cases of more general results about topological vector spaces. In this tract we have tried to present the main theorems as simply and directly as is possible without sacrificing any of their force or generality. It has been our purpose to make the basic ideas and facts of the subject easily accessible. With this in mind, we have assumed only a minimum of knowledge of general topology and linear algebra to start with; the details of what is assumed are to be found at the beginning of the first chapter. After this, new topological concepts am introduced when they are needed. The first four or five chapters contain the fundamental results; here the pace is leisurely. Some of these could have been deduced more concisely from general topological theorems, but we have preferred to keep the treatment self-contained and establish them directly for topological vector spaces, or even for locally convex spaces. From the sixth chapter onwards the proofs are more condensed; here we have allowed ourselves to be guided to some extent by our own interests in the choice of subject matter.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 1964

Количество страниц: 166

Добавлена в каталог: 04.11.2012

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Предметный указатель
 Absolutely convex      4 Absorb      44 Absorbent      5 Adjoint mapping      38 Algebraic, conjugate      25 Algebraic, dual      25 Ascent, finite      145 Baire space      73 Balanced      4 Ball, unit      16 Banach space      60 Banach — Steinhaus theorem      65 70 Barrel      65 Barrelled      65 Base      3 Base of neighbourhoods      7 Base, dual      36 Base, filter      56 Bicontinuous      8 Bilinear, form      31 130 Bilinear, mapping      130 Bipolar      35 Bornological      81 Bounded, mapping      81 Bounded, set      44 Bounded, strongly      70 Bounded, weakly      70 Canonical mapping      77 Category, first      73 Category, second      73 Cauchy, filter      58 Cauchy, sequence      60 Chain      3 Closed set      6 Closure      6 Closure, point of      6 Cluster point      109 Coarser (topology)      7 Compact, mapping      143 Compact, set      52 Compatible      9 complete      59 Complete, fully      111 Completion      101 conjugate      25 Conjugate, mapping      38 continuous      8 Convergence, of filter      56 Convergence, of sequence      55 Convex      4 Convex, envelope      5 Convex, space      10 coordinates      87 Covering      52 Covering, open      52 Dense      6 Descent, finite      145 Determined by seminorms (topology)      15 Direct sum      89 Direct sum, topology      90 Distance      7 distribution      41 Dual      25 Dual, algebraic      25 Dual, mapping      38 Dual, pair      32 Dual, reflexive dual pair      72 Dual, topology of dual pair      34 Eberlein's theorem      109 Eigenvalue      142 Eigenvector      142 Envelope, absolutely convex      5 Envelope, convex      5 Equicontinuous      24 Equicontinuous, convergence (topology of)      137 Equivalent metrics      7 Euclidean topology      37 Extremal point      138 Extremities of line segment      138 Filter      56 Filter, base      56 Filter, Cauchy      58 Filter, elementary      57 Filter, generated      56 Finer, (filter)      56 Finer, (topology)      7 Form, bilinear      130 Form, linear      25 Frechet space      60 Fully complete      111 Gauge      13 Graph      114 Graph, closed graph theorem      116 123 Hahn — Banach theorem      26 29 Hausdorff      7 Homeomorphic      8 Homeomorphism      8 Homomorphism      113 Hypercomplete      125 Hyperplane      25 Induced limit      79 Induced limit, strict      127 Induced topology      8 Injection mapping      88 Interior      6 Interior, point      6 Interior, point of line segment      138 Isomorphic      24 Isomorphism      24 Krein — Milman theorem      138 Krein's theorem      128 Line segment      138 Linear, form      25 Linear, functional      25 Linear, mapping      23 Linearly independent      2 Locally convex      10 Mackey, space      81 Mackey, topology      62 Mapping, bilinear      130 Mapping, linear      23 Maximal      3 Measure, Radon      40 Metric      7 Metric space      7 Metrisable      7 Minimal      3 Montel space      74 n-Dimensional      4 Nearly, closed      111 Nearly, continuous      115 Nearly, open      113 Neighbourhood      6 Neighbourhood of origin      9 Nilpotent      148 Norm      13 Normable      16 Nowhere dense      73 Nuclear      141 open      6 Open covering      52 Open mapping      112 Operation      23 Operator      23 Orthogonal      35 polar      34 Polar topology      46 Precompact      49 Product topology      87 Projection mapping      87 Projective, limit      84 Projective, tensor product topology      132 Projector      97 Quotient      76 Quotient, topology      77 Radon measure      40 Rapid decrease      19 Refinement, filter      56 Reflexive, dual pair      72 Reflexive, space      72 Riesz theory      142 Schauder's theorem      153 Seminorm      12 Separated      7 Separately continuous      136 Small of order U      49 Spectrum      142 Strong topology      47 Subspace, vector      2 Supplement, algebraic      96 Supplement, topological      96 Support, of convex set      139 Support, of distribution      41 Support, of function      18 Support, of measure      41 Tensor product      130 Tensor product, topological      132 Topological, space      6 Topological, vector space      9 Topology, direct sum      90 Topology, Mackey      62 Topology, of -convergence      46 68 Topology, of compact convergence      18 Topology, of compact convergence for all derivatives      19 Topology, of equicontinuous convergence      137 Topology, of uniform convergence      17 46 68 Topology, polar      46 Topology, product      87 Topology, strong      47 Topology, weak      32 Totally bounded      50 Transformation      23 Tychonoff's theorem      64 Ultrafllter      57 Vanishes at infinity      63 Vector subspace      2 Vector subspace, spanned by      2 Weak topology      32
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