Surveys in General Topology

George M. Reed

• Publisher: Academic Press
• Year: 2014
• Print ISBN:
  9780125849609
• eBook ISBN:
  9781483263861
• Topic: Mathematics
• Subtopic: Mathematics General
• Index: Mathematics

Surveys in General Topology presents topics relating to general topology ranging from closed mappings and ultrafilters to covering and separation properties of box products. Ordered topological spaces and the use of combinatorial techniques in functional analysis are also considered, along with product spaces and weakly compact subsets of Banach spaces. Applications of stationary sets in topology are presented as well. Comprised of 15 chapters, this volume begins with an analysis of some of the techniques and results in the area of closed mappings, followed by a discussion on the theory of ultrafilters. The reader is then introduced to the question of when a box product of compact spaces is paracompact, and how badly a box product of compact or metrizable spaces can fail to be normal. Subsequent chapters focus on the transfinite dimension; the properties of metacompactness, submetacompactness, and subparacompactness; the dimension of ordered topological spaces; the use of combinatorial techniques for the treatment and solution of fundamental problems in functional analysis, particularly in the isomorphic theory of Banach spaces; and order-theoretic base axioms. This monograph will be of significant value both to researchers in general topology and to mathematicians outside the field who wish an overview of current topics and techniques.

Table of contents

• Front Cover
• Surveys in General Topology
• Copyright Page
• Table of Contents
• Dedication
• Contributors
• Preface
• Acknowledgments
• Chapter 1. CLOSED MAPPINGS
• Chapter 2. ULTRAFILTERS: AN INTERIM REPORT
• Chapter 3. COVERING AND SEPARATION PROPERTIES OF BOX PRODUCTS
• Chapter 4. TRANSFINITE DIMENSION
• Chapter 5. APPLICATIONS OF STATIONARY SETS IN TOPOLOGY
• Chapter 6. THREE COVERING PROPERTIES
• Chapter 7. ORDERED TOPOLOGICAL SPACES
• Chapter 8. DIMENSION OF GENERAL TOPOLOGICAL SPACES
• Chapter 9. COMBINATORIAL TECHNIQUES IN FUNCTIONAL ANALYSIS
• Chapter 10. ORDER-THEORETIC BASE AXIOMS
• Chapter 11. PRODUCT SPACES
• Chapter 12. S AND L SPACES
• Chapter 13. LARGE CARDINALS FOR TOPOLOGISTS
• Chapter 14. WEAKLY COMPACT SUBSETS OF BANACH SPACES
• Chapter 15. THE DEVELOPMENT OF GENERALIZED BASE OF COUNTABLE ORDER THEORY