Topological Groups and Related Structuresatlantis press, 2008 - 781 Seiten This book presents a large amount of material, both classic and recent (on occasion, unpublished) about the relations of Algebra and Topology. It therefore belongs to the area called Topological Algebra. More specifically, the objects of the study are subtle and sometimes unexpected phenomena that occur when the continuity meets and properly feeds an algebraic operation. Such a combination gives rise to many classic structures, including topological groups and semigroups, paratopological groups, etc. Special emphasis is given to tracing the influence of compactness and its generalizations on the properties of an algebraic operation, causing on occasion the automatic continuity of the operation. The main scope of the book, however, is outside of the locally compact structures, thus distinguishing the monograph from a series of more traditional textbooks.The book is unique in that it presents very important material, dispersed in hundreds of research articles, not covered by any monograph in existence. The reader is gently introduced to an amazing world at the interface of Algebra, Topology, and Set Theory. He/she will find that the way to the frontier of the knowledge is quite short -- almost every section of the book contains several intriguing open problems whose solutions can contribute significantly to the area. |
Inhalt
Compactness and its Generalizations in Topological Groups | 571 |
Actions of Topological Groups on Topological Spaces | 697 |
compacta | 716 |
Andere Ausgaben - Alle anzeigen
Topological Groups and Related Structures A. V. Arkhangelʹskiĭ,Mikhail Tkachenko Eingeschränkte Leseprobe - 2008 |
Topological Groups and Related Structures, An Introduction to Topological ... Alexander Arhangel’skii,Mikhail Tkachenko Eingeschränkte Leseprobe - 2008 |
Häufige Begriffe und Wortgruppen
Abelian topological group algebraic arbitrary C-embedded cardinal Čech-complete Clearly closed subgroup closed subset closure compact group compact Hausdorff compact space compact topological group continuous homomorphism continuous mapping continuous real-valued function converges Corollary countably compact defined Denote dense subgroup Dieudonné complete disjoint example exists a continuous extremally disconnected finite first-countable follows free topological group group F(X group G Gs-set Hausdorff space Hence implies infinite integer isomorphic Lemma Let G Lindelöf locally compact Math metrizable space Moscow space neutral element open neighbourhood open sets open subset P-group P-space paratopological group precompact PROOF Proposition Prove pseudocompact quotient group quotient space Raikov complete satisfying second-countable semigroup semitopological group sequence space G subgroup H subgroup of G subset of G Suppose that G Theorem topological group topology topological product topological space topological subgroup topologically isomorphic Tychonoff space verify w-narrow w₁ zero-dimensional