Topology for Beginners: A Rigorous Introduction to Set Theory, Topological Spaces, Continuity, Separation, Countability, Metrizability, Compactness, C
暫譯: 初學者拓撲學：集合論、拓撲空間、連續性、分離性、公度性、可數性、可度量化、緊緻性與 C 的嚴謹導論

Topology for Beginners consists of a series of basic to intermediate lessons in topology. In addition, all the proofwriting skills that are essential for advanced study in mathematics are covered and reviewed extensively. Topology for Beginners is perfect for

• professors teaching an undergraduate course or basic graduate course in topology.
• high school teachers working with advanced math students.
• students wishing to see the type of mathematics they would be exposed to as a math major.

The material in this pure math book includes:

• 16 lessons consisting of basic to intermediate topics in set theory and topology.
• A problem set after each lesson arranged by difficulty level.
• A complete solution guide is included as a downloadable PDF file.

Topology Book Table Of Contents (Selected) Here's a selection from the table of contents:
Introduction
Lesson 1 - Sets and Subsets
Lesson 2 - Operations on Sets
Lesson 3 - Relations
Lesson 4 - Functions and Equinumerosity
Lesson 5 - Number Systems and Induction
Lesson 6 - Algebraic Structures and Completeness
Lesson 7 - Basic Topology of R and C
Lesson 8 - Continuity in R and C
Lesson 9 - Topological Spaces
Lesson 10 - Separation and Countability
Lesson 11 - Metrizable Spaces
Lesson 12 - Compactness
Lesson 13 - Continuity and Homeomorphisms
Lesson 14 - Connectedness
Lesson 15 - Function Spaces
Lesson 16 - Algebraic Topology