🍩 General Topology

"A topologist is one who doesn't know the difference between a doughnut and a coffee cup."

📊 Course Metadata

• Opening Unit: School of Mathematical Sciences
• Prerequisites: Mathematical Analysis
• Course Nature: Core Undergraduate Course for Mathematics Majors

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📚 References

This course does not use PPT or other digital presentation tools; it is taught entirely via hand-written blackboard lectures by the professor.

1. James R. Munkres, Topology (2nd Edition)

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🗺️ Syllabus & Navigation

The following is a detailed directory of the notes and lecture materials for this course:

Part I: Foundations of Set Theory and Topological Spaces

• Chapter 1: Set Theory and Foundations of Logic

• Chapter 2: Functions and Relations

• Chapter 3: Countable and Uncountable Sets

• Chapter 4: Open Sets and Topological Structures

Part II: Constructions of Topological Spaces and Continuity

• Chapter 5: Induced Topologies and Basic Topological Operations

• Chapter 6: Closures, Continuity, and Homeomorphisms

Part III: Core Topological Invariants and Space Properties

• Chapter 7: Mappings in Product Spaces and Connectedness

• Chapter 8: Compactness

• Chapter 9: Compactness in Euclidean Spaces

• Chapter 10: Sequential Compactness

• Chapter 11: One-Point Compactification

• Chapter 12: Countability Axioms

• Chapter 13: Separation Axioms

Part IV: 📝 Selected Solutions

• Exercises 01: HW01 & HW02

• Exercises 02: HW03 & HW04

• Exercises 03: HW05 & HW06

• Exercises 04: HW07 & HW08 & HW09

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📝 Notes & Formatting Details

Construction Complete

This page is now substantially complete. Long theorems and exercise solutions in the notes feature a folded box design. If you spot any typos, please feel free to raise an Issue or contact me directly for corrections!

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