Quotient spaces, visually understood

Quotient spaces until recently gave me a great deal of trouble. I had no intuition for them, and no image to latch on to.

Until I started taking algebraic topology.

I learned that the quotient under an equivalence relation is like gluing 2 spaces together, where the points you stick together are identified with each other.

This excellent image illustrates the idea for the attaching map of two topological spaces. The requirement that \(f\) be a homeomorphism is also clearer from the picture.

Related Posts

Just because 2 things are dual, doesn't mean they're just opposites

Boolean Algebra, Arithmetic POV

discontinuous linear functions

Continuous vs Bounded

Minimal Surfaces

November 2, 2023

NTK reparametrization

Kate from Vancouver, please email me

ChatGPT Session: Emotions, Etymology, Hyperfiniteness

Some ChatGPT Sessions