Topological Spaces Courses and Certifications

Hausdorff Center for Mathematics

Iosif Petrakis - Bishop Spaces and the Problem of Constructivizing General Topology

Explores Bishop spaces as a constructive alternative to classical topology, overcoming obstacles in continuity and compactness. Presents key results and connections to other constructive space notions.

• YouTube
• 34 minutes
• On-Demand
• Free Video

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
• On-Demand
• 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
• On-Demand
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

The Weak Extension Principle and Its Coarse Version

Explore the weak Extension Principle for Čech-Stone remainders, its generalizations to locally compact metrizable spaces, and a coarse geometric version yielding rigidity results for Higson coronas.

• YouTube
• 44 minutes
• On-Demand
• Free Video

Insights into Mathematics

Topological Spaces and Manifolds - Differential Geometry Lecture 24

Explore topological spaces and manifolds through neighborhood systems and open sets. Learn key concepts, solve problems, and understand the foundations of continuous space theory in modern mathematics.

• YouTube
• 50 minutes
• On-Demand
• 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
• On-Demand
• Free Video

点集拓扑

该课在数学人才培养过程中有着重要的作用。该课对极限与连续做了最一般的推广。学完该课再回望微积分有一览众山小之感。

• XuetangX
• On-Demand
• 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
• On-Demand
• Free Certificate

Applied Algebraic Topology Network

Hubert Wagner - Topological Data Analysis in Non-Euclidean Spaces

Explore topological data analysis in non-Euclidean spaces, focusing on techniques for applying TDA tools and their applications in detecting neural network backdoor attacks.

• YouTube
• 57 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Topological and Combinatorial Models of Directed Path Spaces

Explore topological and combinatorial models for directed path spaces in concurrency theory, focusing on methods to analyze execution paths and state spaces in computer science.

• YouTube
• 1 hour 25 minutes
• On-Demand
• Free Video

Kavli Institute for Theoretical Physics

QED Quantum Fluctuations in the Presence of Half-Spaces Filled With Topological Insulators

Explores quantum electrodynamic fluctuations near topological insulators, discussing implications for Casimir interactions and heat transfer in various materials and experimental challenges.

• YouTube
• 48 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

On the Rational Topological Complexity of Coformal Elliptic Spaces

Explore rational topological complexity bounds for elliptic spaces, focusing on coformal cases where it aligns with rational homotopy dimension.

• YouTube
• 47 minutes
• On-Demand
• Free Video

IMSA

Topological Recursion for Hurwitz Theory and Intersection Theory of Moduli Spaces of Curves

Explore topological recursion in Hurwitz theory and its connections to moduli spaces of curves. Discover ELSV-type formulae and their impact on understanding ramifications and cohomological field theories.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

ICTP Mathematics

Virtual Topological Invariants of Moduli Spaces of Sheaves on Surfaces

Explore virtual topological invariants of moduli spaces, focusing on multiplicative classes, convergence, and residual formulas in sheaf theory on surfaces.

• YouTube
• 1 hour
• On-Demand
• Free Video

ICTP Mathematics

Virtual Topological Invariants of Moduli Spaces of Sheaves on Surfaces

Explore virtual topological invariants of moduli spaces, focusing on sheaves on surfaces. Learn about ischemic points, Euler numbers, and perfect obstruction theory.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video