Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Geometric group theory. --- Polish spaces (Mathematics). --- Topological groups. --- Transformation groups.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book provides a general framework for doing geometric group theory for many non-locally-compact topological transformation groups that arise in mathematical practice, including homeomorphism and diffeomorphism groups of manifolds, isometry groups of separable metric spaces and automorphism groups of countable structures. Using Roe's framework of coarse structures and spaces, the author defines a natural coarse geometric structure on all topological groups. This structure is accessible to investigation, especially in the case of Polish groups, and often has an explicit description, generalising well-known structures in familiar cases including finitely generated discrete groups, compactly generated locally compact groups and Banach spaces. In most cases, the coarse geometric structure is metrisable and may even be refined to a canonical quasimetric structure on the group. The book contains many worked examples and sufficient introductory material to be accessible to beginning graduate students. An appendix outlines several open problems in this young and rich theory.

Geometric group theory. --- Polish spaces (Mathematics) --- Transformation groups. --- Topological groups.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Polish spaces (Mathematics) --- Metric spaces. --- Isomorphisms (Mathematics) --- Espaces polonais (Mathématiques) --- Espaces métriques --- Isomorphismes (Mathematiques) --- Metric spaces --- Espaces polonais (Mathématiques) --- Espaces métriques

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Polish spaces (Mathematics). --- Set theory. --- Polish spaces (Mathematics) --- Aggregates --- Classes (Mathematics) --- Ensembles (Mathematics) --- Mathematical sets --- Sets (Mathematics) --- Theory of sets --- Logic, Symbolic and mathematical --- Mathematics --- Groups, Polish (Mathematics) --- Polish groups (Mathematics) --- Polish spaces --- Polish topological spaces --- Spaces, Polish (Mathematics) --- Metric spaces --- Set theory

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book lays the foundations for an exciting new area of research in descriptive set theory. It develops a robust connection between two active topics: forcing and analytic equivalence relations. This in turn allows the authors to develop a generalization of classical Ramsey theory. Given an analytic equivalence relation on a Polish space, can one find a large subset of the space on which it has a simple form? The book provides many positive and negative general answers to this question. The proofs feature proper forcing and Gandy-Harrington forcing, as well as partition arguments. The results include strong canonization theorems for many classes of equivalence relations and sigma-ideals, as well as ergodicity results in cases where canonization theorems are impossible to achieve. Ideal for graduate students and researchers in set theory, the book provides a useful springboard for further research.

Set theory. --- Ramsey theory. --- Polish spaces (Mathematics) --- Groups, Polish (Mathematics) --- Polish groups (Mathematics) --- Polish spaces --- Polish topological spaces --- Spaces, Polish (Mathematics) --- Metric spaces --- Combinatorial analysis --- Graph theory --- Aggregates --- Classes (Mathematics) --- Ensembles (Mathematics) --- Mathematical sets --- Sets (Mathematics) --- Theory of sets --- Logic, Symbolic and mathematical --- Mathematics