Open problems in topology. II / edited by Elliott Pearl.

Format:

Book

Contributor:

Pearl, Elliott.

Language:

English

Subjects (All):

Topology.

Geometry.

Physical Description:

1 online resource (777 p.)

Edition:

1st ed.

Other Title:

Open problems in topology 2

Place of Publication:

Amsterdam ; Oxford : Elsevier, 2007.

Language Note:

English

Summary:

This volume is a collection of surveys of research problems in topology and its applications. The topics covered include general topology, set-theoretic topology, continuum theory, topological algebra, dynamical systems, computational topology and functional analysis.* New surveys of research problems in topology* New perspectives on classic problems* Representative surveys of research groups from all around the world

Contents:

Front Cover; Open Problems in Topology II; Copyright Page; Preface; Table of Contents; Part 1. General Topology; Chapter 1. Selected ordered space problems; 1. Introduction; 2. A few of our favorite things; References; Chapter 2. Problems on star-covering properties; Introduction; Compactness-type properties; Lindelöf-type properties and cardinal functions; Paracompactness-type properties; Property (a); References; Chapter 3. Function space topologies; 1. Splitting and admissible topologies; 2. The greatest splitting, compact-open, and Isbell topologies; References

Chapter 4. Spaces and mappings: special networksIntroduction; Mappings; k-networks and weak bases; Spaces determined or dominated by certain covers; Products of k-spaces having certain k-networks; References; Chapter 5. Extension problems of real-valued continuous functions; 1. Introduction; 2. C-embedding versus C*-embedding; 3. p-embedding and pZ-embeddings; 4. Miscellaneous questions; References; Chapter 6. LS(k)-spaces; References; Chapter 7. Problems on (ir)resolvability; Introduction. Resolvability hierarchy; Resolvability of connected spaces; Baire property and a problem of Katetov

Groups and homogeneous spacesCompactness, products, miscellaneous questions; Structure resolvability; Literature; References; Chapter 8. Topological games and Ramsey theory; Introduction; 1. Basic concepts; 2. The point-picking ganes; 3. Modifications of the point-picking games; 4. The set-picking games; 5. Further restrictions on ONE; 6. Banach-Mazur games; 7. The length of games; 8. Memory restrictions on the winning player; 9. Ramsey theory; References; Chapter 9. Selection principles and special sets of reals; 1. Introduction; 2. The Scheepers Diagram problem

3. Examples without special set-theoretic hypotheses4. Examples from CH or MA; 5. The d-property; 6. Preservation of properties; 7. Modern types of covers; 8. Splittability; 9. Function spaces and local-global principles; 10. Topological groups; 11. Cardinal characteristics of the continuum; 12. Additional problems and other special sets of reals; References; Part 2. Set-theoretic Topology; Chapter 10. Introduction: Twenty problems in set-theoretic topology; References; Chapter 11. Thin-tall spaces and cardinal sequences; 1. Introduction; 2. Spaces of countable height

3. Spaces of height ?2; 6. A basic construction; 7. Forcing an LCS space; 8. Final remarks; References; Chapter 12. Sequential order; References; Chapter 13. On D-spaces; Introduction; Questions about D-spaces; Stickyness; General remarks; References; Chapter 14. The fourth head of ßN; 1. Trivial continuous maps; 2. A partial result; 3. Rigidity phenomena for quotients P(N)/I; 4. Further results; 5. Conclusion; References; Chapter 15. Are stratifiable spaces M1?; 1. Equivalent questions; 2. Related classes and partial results

3. Function spaces and a possible counterexample

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

1-281-00381-6

9786611003814

0-08-047529-9

OCLC:

469445302