图书简介
Point-Set Topology with Topics: Basic General Topology for Graduate Studies can be used as an introduction to a general topology course for both undergraduate and graduate level courses. Presenting topological concepts which apply directly to functional analysis, this book will also be of interest to scholars working in those fields.Part I contains a summary of normed vector spaces and metric spaces, which will ease the reader into the main subject matter of general topology. Parts II to VI form the core of the text, presenting in diverse ways and at a range of levels the material usually covered in basic general topology courses. After having worked through the most fundamental concepts of topology, the reader will be exposed, in part VII, to more specialized or advanced topics of point-set topology. These appear in the form of a sequence of chapters, many of which can be studied independently.Each chapter is followed by a collection of ’concept review’ questions whose answers can usually be found in the main body of the text. These questions highlight the main concepts presented in that chapter. They serve to attract the attention of the reader to ideas that are often overlooked when first encountered. The efforts required in answering such questions correctly will provide the student with the ability to solve the more complex problems collected at the end of each section.Key FeaturesThere are "concept review" questions at the end of each chapter to facilitate understanding and reinforce learning, the answers to which are found in the main body of the textThere are exercise questions at the end of each sectionInstructors are able to choose from a variety of topics in this textbook, which can be assigned to graduate students for class presentations
Norms and Metrics: Norms on Vector Spaces; Metrics on Sets; Topological Spaces: Fundamental Concepts: A Topology on a Set; Set Closures, Interiors and Boundaries; Bases of Topological Spaces; Continuity on Topological Spaces; Product Spaces; The Quotient Topology; Topological Spaces: Separation Axioms: Separation with Open Sets; Separation with Continuous Functions; Limit Points in Topological Spaces: Limit Points in First Countable Spaces; Limit Points of Nets; Limit Points of Filters; Compact Spaces and Relatives: Compactness: Definition and Basic Properties; Countably Compact Spaces; Lindelöf Spaces; Sequentially and Feebly Compact Spaces; Locally Compact Spaces; Paracompact Topological Spaces; The Connected Property: Connected Spaces and Properties; Topics: Compactifications of Completely Regular Spaces; Singular Sets and Singular Compactifications; On C-Embeddings and Pseudocompactness; Realcompact Spaces; Perfect Functions; Perfect and Freudenthal Compactifications; Spaces Whose Elements are Sequences; Completing Incomplete Metric Spaces; The Uniform Space and the Uniform Topology; The Stone-Weierstrass Theorem; Metrizability; The Stone Space; Baire Spaces; The Class of F-Spaces; Appendix; Bibliography; Index
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