I took a linear algebra course. Maybe I need to restudy but I would rather have links to exact chapters than reading the whole thing, as I don't see a direct path from the linear algebra I studied to the topology concepts and geometry here. Specifically there weren't any curves in linear algebra. Ex 4.10 and 4.11 here: http://planning.cs.uiuc.edu/node143.html
Are examples of things that are hard for me to understand. Especially that 2d picture in 4.11
You have to study quite a lot of linear algebra before you can tackle functional analysis, the subject which includes the study of topological vector spaces. I don't know anything about robotics, however, so I don't know how functional analysis would apply, if at all.
Functional analysis shows up all over the place. Everywhere you can take a Fourier transform, you can use functional analysis. For robotics, control theory and computer vision both come to mind.
Are examples of things that are hard for me to understand. Especially that 2d picture in 4.11