Topological Spaces Courses and Certifications

IIT (ISM) Dhanbad;  NPTEL

Essentials of Topology

Develops rigorous foundations for higher mathematics through topological spaces, continuity, connectedness, compactness, and separation axioms.

• Swayam
• 12 weeks
• Available until Oct 9, 2026
• Free Online Course

An introduction to Point-Set-Topology Part - II

Advanced point-set topology through compactness, metrization, compactifications, function-space topologies, and ordinal-topology counterexamples.

• Swayam
• 12 weeks
• Available until Oct 9, 2026
• Free Online Course

NPTEL-NOC IITM

Mathematical Preliminaries - Basics of Point-Set Topology 1

Discover topological spaces, continuous maps, homeomorphisms, and topological invariants in this foundational exploration of point-set topology concepts.

• YouTube
• 31 minutes
• Self-Paced
• Free Video

NPTEL-NOC IITM

Mathematical Preliminaries - Basics of Point-Set Topology 2

Explore topological spaces, continuous maps, homeomorphisms, and topological invariants in this foundational mathematics lecture covering essential point-set topology concepts.

• YouTube
• 34 minutes
• Self-Paced
• Free Video

Math Sorcerer

Introduction to Counterexamples in Topology - Strange Topological Spaces

Explore the fascinating world of topology through unique and peculiar topological spaces, understanding fundamental concepts and counterexamples in mathematical theory.

• YouTube
• 11 minutes
• Self-Paced
• Free Video

Introduction to Metric Spaces

Work through metric spaces: metrics, open and closed sets, topological continuity, function spaces, completeness, and compactness in Rⁿ and general metric spaces.

• MIT OpenCourseWare
• Self-Paced
• Free Online Course

Surfaces

4 ratings at OpenLearn

Surfaces are a special class of topological spaces that crop up in many places in the world of mathematics. In this free course, you will learn to classify surfaces and will be introduced to such ...

• OpenLearn
• 20 hours
• Self-Paced
• Free Certificate

Metric spaces and continuity

This free course contains an introduction to metric spaces and continuity. The key idea is to use three particular properties of the Euclidean distance as the basis for defining what is meant by a ...

• OpenLearn
• 16 hours
• Self-Paced
• Free Certificate

Utrecht Geometry Centre

Introduction to Algebraic Topology

Discover fundamental concepts in algebraic topology including fundamental groups, van Kampen's theorem, and surface classification in this comprehensive introduction.

• YouTube
• 1 hour 36 minutes
• Self-Paced
• Free Video

Algebraic Topology - Algebraic Invariants of Spaces

Explore algebraic invariants of topological spaces including fundamental groups, higher homotopy groups, homology, and cohomology with their homotopy invariance properties.

• YouTube
• 55 minutes
• Self-Paced
• Free Video

Michael Penn

A Space Where Nothing Is Prime

Explore the fascinating mathematical concept of prime ideals in ring theory and discover spaces where traditional notions of primality break down.

• YouTube
• 32 minutes
• Self-Paced
• Free Video

Michael Penn

A Complete Explanation of Hausdorff Spaces - Live Example

Discover the fundamental properties of Hausdorff spaces through clear explanations and practical examples in this concise topology lesson.

• YouTube
• 12 minutes
• Self-Paced
• Free Video

The Bright Side of Mathematics

Manifolds

An introduction to manifolds through topology, covering topological spaces, projective space, local Euclidean structure, and smooth structures.

• YouTube
• 2 hours 30 minutes
• Self-Paced
• Free Video

IMSC;  NPTEL

An invitation to Topology

Explore how topology formalizes abstract spaces and extends limits, continuity, connectedness, and compactness.

• Swayam
• 12 weeks
• Not Currently Offered
• Free Online Course

Metric Spaces

Develops metric-space topology by extending open sets, convergence, compactness, and continuity from the real line to arbitrary spaces.

• Swayam
• 12 weeks
• No Longer Offered
• Free Online Course