位相群と構造<br>Topological Guide and Related Structures (Atlantis Studies in Mathematics)

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位相群と構造
Topological Guide and Related Structures (Atlantis Studies in Mathematics)

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  • 製本 Hardcover:ハードカバー版/ページ数 781 p.
  • 言語 ENG
  • 商品コード 9789078677062
  • DDC分類 514

Table of Contents

Foreword                                           v
Introduction to Topological Groups and 1 (89)
Semigroups
Some algebraic concepts 1 (11)
Groups and semigroups with topologies 12 (6)
Neighbourhoods of the identity in 18 (8)
topological groups and semigroups
Open sets, closures, connected sets and 26 (11)
compact sets
Quotients of topological groups 37 (9)
Products, Σ-products, and 46 (16)
σ-products
Factorization theorems 62 (4)
Uniformities on topological groups 66 (15)
Markov's theorem 81 (6)
Historical comments to Chapter 1 87 (3)
Right Topological and Semitopological Groups 90 (44)
From discrete semigroups to compact 91 (6)
semigroups
Idempotents in compact semigroups 97 (12)
Joint continuity and continuity of the 109(11)
inverse in semitopological groups
Pseudocompact semitopological groups 120(9)
Cancellative topological semigroups 129(2)
Historical comments to Chapter 2 131(3)
Topological groups: Basic constructions 134(82)
Locally compact topological groups 134(13)
Quotients with respect to locally compact 147(4)
subgroups
Prenorms on topological groups, 151(11)
metrization
w-narrow and w-balanced topological groups 162(11)
Groups of isometries and groups of 173(8)
homeomorphisms
Raikov completion of a topological group 181(12)
Precompact groups and precompact sets 193(9)
Embeddings into connected, locally 202(10)
connected groups
Historical comments to Chapter 3 212(4)
Some Special Classes of Topological Groups 216(69)
Ivanovskij-Kuz'minov Theorem 217(9)
Embedding Dω1 in a non-metrizable 226(4)
compact group
Cech-complete and feathered topological 230(19)
groups
P-groups 249(6)
Extremally disconnected topological and 255(9)
quasitopological groups
Perfect mappings and topological groups 264(9)
some convergence phenomena in topological 273(9)
groups
Historical comments to Chapter 4 282(3)
Cardinal Invariants of Topological Groups 285(60)
More on embeddings in products of 286(10)
topological groups
Some basic cardinal invariants of 296(7)
topological groups
Lindelof Σ-groups and Nagami number 303(13)
Cellularity and weak precalibres 316(7)
o-tightness in topological groups 323(6)
Steady and stable topological groups 329(7)
Cardinal invariants in paratopological 336(7)
and semitopological groups
Historical comments to Chapter 5 343(2)
Moscow Topological Groups and Completions 345(64)
of Groups
Moscow spaces and E-embeddings 346(5)
Moscow spaces, P-spaces, and extremal 351(3)
disconnectedness
Products and mappings of Moscow spaces 354(5)
The breadth of the class of Moscow groups 359(7)
When the Dieudonne completion of a 366(8)
topological group is a group?
Pseudocompact groups and their completions 374(4)
Moscow groups and the formula ν(X 378(7)
× Y) = νX × νY
Subgroups of Moscow groups 385(3)
Pointwise pseudocompact and feathered 388(7)
groups
Bounded and C-compact sets 395(12)
Historical comments to Chapter 6 407(2)
Free Topological Groups 409(106)
Definition and basic properties 409(15)
Extending pseudometrics from X to F(X) 424(19)
Extension of metrizable groups by compact 443(3)
groups
Direct limit property and completeness 446(7)
Precompact and bounded sets in free groups 453(3)
Free topological groups on metrizable 456(20)
spaces
Nummela-Pestov theorem 476(6)
The direct limit property and countable 482(8)
compactness
Completeness of free Abelian topological 490(9)
groups
M-equivalent spaces 499(12)
Historical comments to Chapter 7 511(4)
R-Factorizable Topological Groups 515(56)
Basic properties 515(11)
Subgroups of R-factorizable groups. 526(6)
Embeddings
Dieudonne completion of R-factorizable 532(3)
groups
Homomorphic images of R-factorizable 535(3)
groups
Products with a compact factor and 538(12)
m-factorizability
R-factorizability of P-groups 550(12)
Factorizable groups and projectively 562(3)
Moscow groups
Zero-dimensionality of R-factorizable 565(4)
groups
Historical comments to Chapter 8 569(2)
Compactness and its Generalizations in 571(126)
Topological Groups
Krein-Milman Theorem 571(5)
Gel'fand-Mazur Theorem 576(5)
Invariant integral on a compact group 581(13)
Existence of non-trivial continuous 594(10)
characters on compact Abelian groups
Pontryagin-van Kampen duality theory for 604(6)
discrete and for compact groups
Some applications of Pontryagin-van 610(11)
Kampen's duality
Non-trivial characters on locally compact 621(3)
Abelian groups
Varopoulos' theorem: the Abelian case 624(9)
Bohr topology on discrete Abelian groups 633(30)
Bounded sets in extensions of groups 663(3)
Pseudocompact group topologies on Abelian 666(9)
groups
Countably compact topologies on Abelian 675(17)
groups
Historical comments to chapter 9 692(5)
Actions of Topological Groups on 697(38)
Topological Spaces
Dugundji spaces and 0-soft mappings 697(11)
Continuous action of topological groups 708(8)
on spaces
Uspenskij's theorem on continuous 716(7)
transitive actions of ω-narrow
groups on compacta
Continuous actions of compact groups and 723(9)
some classes of spaces
Historical comments to Chapter 10 732(3)
Bibliography 735(20)
List of symbols 755(2)
Author Index 757(4)
Subject Index 761