Formalization of various notions of convergence

Hello,

I wrote a note on notions of convergence of sequences of functions in mathematics.

My goal was to see by myself if many definitions were possible.

I did found quite a few definitions at the end.

Maybe the approximate notions of convergence would be more interesting to computer scientists than mathematicians.

I was expecting to write 3 pages or so, and my note is 9 pages long now.

I thought this note would be better completed as a package of definitions and proofs in Rocq or LEAN. And that it could maybe be a good exercise for students to code it in Rocq.

Here are the links if you want to check if it can be interesting.

French version:

English version:

Best regards,

Laurent Lyaudet