Counterexamples in Topology by Steen and Seebach

  • Thread starter mynameisfunk
  • Start date
  • Tags
    Topology
In summary: The Banach Space Theorem Continuity Immunity to Metrization Derivatives Differentiability Differentiable Functions and Differentiable Operators Derivative Calculus Partial Differential Equations Linear AlgebraSummaryIn summary, this book is a comprehensive guide to topology, covering topics such as set theory, metric spaces, topological spaces, and functions. It provides thorough explanations of key concepts and provides numerous examples and problems to help students better understand the material.

For those who have used this book

  • Lightly Recommend

    Votes: 0 0.0%
  • Lightly don't Recommend

    Votes: 0 0.0%
  • Strongly don't Recommend

    Votes: 0 0.0%

  • Total voters
    3
  • #1
mynameisfunk
125
0
Hey. Was wondering if anyone had used this or had any feedback on whether this book was any good. I am having a slight schedule conflict with advanced calculus next semester and was considering taking topology. They use this book. On Amazon, there are only 2 reviews which are at opposite extreme ends of the spectrum. If the book is good, I may go ahead and take the course, if it's not, then I may just have to be 15 minutes late to class every day so I can continue studying Rudin for another semester.
 
Physics news on Phys.org
  • #2

Table of Contents:
Code:
[LIST]
[*] Preface
[*] Basic Definitions
[LIST]
[*] General Introduction
[*] Separation Axioms
[*] Compactness
[*] Connectedness
[*] Metric Spaces
[/LIST]
[*] Counterexamples
[*] Appendices
[LIST]
[*] Special Reference Charts
[*] General Reference Chart
[*] Problems
[*] Notes
[*] Bibliography
[/LIST]
[/LIST]
 
Last edited by a moderator:
  • #3

Table of Contents:
Code:
[LIST]
[*] Set Theory and Metric Spaces
[LIST]
[*] Set Theory
[*] Metric Spaces
[/LIST]
[*] Topological Spaces
[LIST]
[*] Fundamental Concepts
[*] Neighborhoods
[*] Bases and subbases
[/LIST]
[*] New Spaces from Old
[LIST]
[*] Subspaces
[*] Continuous Functions
[*] Product Spaces; Weak Topologies
[*] Quotient Spaces
[/LIST]
[*] Convergence
[LIST]
[*] Inadequacy of Sequences
[*] Nets
[*] Filters
[/LIST]
[*] Separation and Countability
[LIST]
[*] The separation axioms
[*] Regularity and Complete Regularity
[*] Normal Spaces
[*] Countability Properties
[/LIST]
[*] Compactness
[LIST]
[*] Compact Spaces
[*] Locally Compact Spaces
[*] Compactification
[*] Paracompactness
[*] Products of Normal Spaces
[/LIST]
[*] Metrizable Spaces
[LIST]
[*] Metric Spaces and Metrizable Spaces
[*] Metrization
[*] Complete Metric Spaces
[*] The Baire Theorem
[/LIST]
[*] Connectedness
[LIST]
[*] Connected Spaces
[*] Pathwise and Local Connectedness
[*] Continua
[*] Totally Disconnected Spaces
[*] The Cantor Set
[*] Peano Spaces
[*] The Homotopy Relation
[*] The Fundamental Group
[*] [itex]\Pi_1(S^1)[/itex]
[/LIST]
[*] Uniform Spaces
[LIST]
[*] Diagonal Uniformities
[*] Uniform Covers
[*] Uniform Products and Subspaces; Weak Uniformities
[*] Uniformizability and Uniform Metrizability
[*] Complete Uniform Spaces; Completion
[*] Proximity Spaces
[*] Compactness and Proximities
[/LIST]
[*] Function Spaces
[LIST]
[*] Pointwise Convergence; Uniform Convergence
[*] The Compact-Open Topology and Uniform Convergence on Compacta
[*] The Stone-Weierstrass Theorem
[/LIST]
[/LIST]
 
Last edited by a moderator:

1. What is the purpose of "Counterexamples in Topology by Steen and Seebach"?

The purpose of "Counterexamples in Topology" is to provide a comprehensive collection of counterexamples in the field of topology. It serves as a reference for students and researchers to better understand the concepts of topology by presenting examples that illustrate the limitations and exceptions to theorems and definitions.

2. Who are the authors of "Counterexamples in Topology by Steen and Seebach"?

"Counterexamples in Topology" was written by Lynn Arthur Steen and J. Arthur Seebach Jr. Both authors are mathematicians who have made significant contributions to the field of topology and have taught at various universities.

3. Is "Counterexamples in Topology" suitable for beginners in topology?

While "Counterexamples in Topology" is a valuable resource for all levels of topology, it is not recommended for beginners. This book assumes a certain level of familiarity with topology concepts and is best suited for advanced undergraduate or graduate students.

4. How is the information organized in "Counterexamples in Topology"?

The book is divided into three parts: general topology, algebraic topology, and geometric topology. Each part is further divided into chapters, with each chapter focusing on a specific topic. Within each chapter, the counterexamples are presented in a clear and organized manner, with detailed explanations and diagrams.

5. Can "Counterexamples in Topology" be used as a textbook for a topology course?

While "Counterexamples in Topology" is not meant to be a textbook, it can be used as a supplement to a topology course. It can be used to provide students with additional examples and counterexamples to enhance their understanding of the subject. However, it is not recommended as the main textbook for a topology course.

Similar threads

  • Science and Math Textbooks
Replies
7
Views
3K
  • Science and Math Textbooks
Replies
10
Views
6K
  • Science and Math Textbooks
Replies
11
Views
2K
Replies
3
Views
1K
  • Science and Math Textbooks
Replies
4
Views
4K
  • Science and Math Textbooks
Replies
8
Views
5K
  • Science and Math Textbooks
2
Replies
38
Views
6K
  • Science and Math Textbooks
Replies
10
Views
6K
  • Science and Math Textbooks
Replies
5
Views
3K
  • Science and Math Textbooks
Replies
5
Views
3K
Back
Top