Topology for Beginners: A Rigorous Introduction to Set Theory, Topological Spaces, Continuity, Separation, Countability, Metrizability, Compactness, Connectedness, Function Spaces, and Algebraic Topology

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