Counterexamples in Topology by Steen and Seebach

[mynameisfunk]

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.

 

[micromass]

• Author: Lynn Arthur Steen and J. Arthur Seebach, Jr.
• Title: Counterexamples in Topology
• Amazon link https://www.amazon.com/dp/048668735X/?tag=pfamazon01-20
• Prerequisities: Set theory and point-set topology
• Level: Undergrad

Table of Contents:

[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]

 

[micromass]

• Author: Stephen Willard
• Title: Topology
• Amazon link https://www.amazon.com/dp/0486434796/?tag=pfamazon01-20
• Prerequisities: Undergrad analysis and set theory
• Level: Grad

Table of Contents:

[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]