The Real Projective Space is an example of an abstract (smooth) manifold

Yet another classical example of an abstract smooth manifold

Local Coordinates and the Local Immersion Theorem Explained

After struggling through these topics, I thought it best to write a piece about them

Solutions To Some Topology Problems

I like having my mathematics organized / in one place so I decided to write up some solutions

How the set of n by n orthogonal matrices forms a lie group.

Some knowledge of linear algebra and basic group theory is required!