Topological Spaces and Manifolds - Differential Geometry Lecture 24

Explore the fundamental concepts of topological spaces and manifolds in this comprehensive lecture from the Differential Geometry series. Delve into the definition of topological spaces through neighborhood systems and open set collections. Examine the traditional approach to these theories while considering their limitations, particularly regarding infinite sets. Learn through practical examples, problem-solving exercises, and discussions on continuous space theory. Gain insights into defining topological spaces for different variables and understand the historical context of these mathematical concepts in the early 21st century.

Introduction
Topologies space 20th Century
Open sets systems
Example on Open set
Problem and solving
Exercises
Define two Topological spaces for x and y