Topology

Anyone has any recommendations for textbooks to read related to Topology?

Everyone can Google topology or spend a little time surfing online to get a general outline of any field of knowledge—including this one.
But if you’ll indulge me, I’d like to offer a puzzle to stretch the meaning of topology more profoundly:
What is the application of topology in this clip?
https://www.facebook.com/reel/2386881401697808