Chapter 1: Introduction to Topology
1.1 Characteristics of topology
1.2 Origins of Topology
1.3 Prerequisites for Understanding Topology: Set Theory
1.4 Set operations: union, intersection, difference
1.5 Cartesian product
1.6 Function
1.7 Equivalence Relations

Chapter 2: Straight Lines and Planes
2.1 Upper and lower bounds
2.2 Finite and infinite sets
2.3 Open and closed sets on the real line
2.4 Reduced interval summary
2.5 flat
Simple history of mathematics

Chapter 3 Distance Space
3.1 Definition and examples of metric space
3.2 Open and closed sets in metric space
3.3 Internal, alveolar, and border
3.4 Continuous functions
3.5 Equivalence in distance space
3.6 New space derived from existing space
3.7 Complete distance space
Simple history of mathematics

Chapter 4 Topological Space
4.1 Definitions and Examples
4.2 Internal, alveolar, and border
4.3 Basis and Partial Basis
4.4 Continuity and topological equivalence
4.5 Subspace
Simple history of mathematics

Chapter 5 Connectivity
5.1 Connected and unconnected spaces
5.2 Theorem on Connectivity
5.3 Connected subsets on the real line
5.4 Applications of Connectivity
5.5 Path connection space
5.6 Locally Connected Space and Locally Path-Connected Space
Simple history of mathematics

Chapter 6 Compactness
6.1 Compact Space and Its Subspaces
6.2 Compactness and continuity
6.3 Properties related to compactness
6.4 One-point compactness
6.5 Cantor set
Simple history of mathematics

Chapter 7: Product Space and Parallel Space
7.1 Finite product spaces
7.2 Extension of the product space
7.3 Comparison between phases
7.4 Commercial space
7.5 Surfaces and Manifolds
Simple history of mathematics

Chapter 8 Separation Properties and Distance
8.1 T_0, T_1, T_2 space
8.2 Regular space
8.3 Regular space
8.4 Separation using continuous functions
8.5 Distance
8.6 Stone-Cech compaction
Simple history of mathematics

Chapter 9 Basic Groups
9.1 The essence of algebraic topology
9.2 Basic Group
9.3 Fundamental group of S^1
9.4 Additional examples of basic groups
9.5 Browser Fixed Point Theorem and Related Results
9.6 Categories and Hamza
Simple history of mathematics

Appendix A Group
Appendix B List of Symbols
Appendix C Recommended Reading
Appendix D References

An introductory book on topology that covers the history of topology from simple examples.

Topology is the study of properties that are maintained when an object is continuously transformed.
Introductory courses in topology mainly cover general topology (point-set topology), focusing on connectivity and continuity in a certain space.
Since these concepts are somewhat abstract when 'distance' is excluded, this book covers topological concepts step by step, starting from straight lines and planes that are familiar to us, so that even beginners in topology can learn in an enjoyable way.
Through the [Simple History of Mathematics] in each chapter, you can examine which topologists left their mark on the world of mathematics in the 1900s and what circumstances they were involved in during that time.