Our study of point set topology (also known as elementary topology & general topology) starts with definitions of open sets, closed sets, the topological spaces, closed-finite topologies, T0 spaces and T1 spaces. We also prove a fundamental result classifying closed sets.
This work follows the book:
Topology Without Tears
http://u.math.biu.ac.il/~megereli/top...
The course could also be considered to be an extension of the `topology for beginners' lectures for viewers who prefer a more rigorous exposition.
https://sites.google.com/site/richard...