[hanzoganz]

That is simply a correspondence relation, not a function, you are right about it. So, it is simpler. Just look for correspondence relations, if you want a deeper knowledge go to number theory or abstract algebra. Yes, algebra better. After algebra, you can go to topology.
Any good book on abstrac or modern algebra will have examples on what you are thinking about.

[AntonioLao]

Originally Posted by hanzoganz

Any good book on abstrac or modern algebra will have examples

Thanks. I looked at fiber bundles, if not mistaken, these are still 1-1 correspondence.