trees and plants
Hello. How to think in abstract spaces?Like manifolds? Or metric spaces? Or function or Banach spaces? Are they not just generalisations of the usual 2d or 3d Euclidean spaces we know? So they could be studied by generalising or extending things we know from 2d or 3d euclidean spaces and if they have curvature or other features that we can see or know in 2 dimensions or 3 dimensions like projections, derivatives, integrals, limits and others? Generally, that is the way all abstract spaces in mathematics are studied or thought? By thinking of the things we know from 2 or 3 dimensions and generalising or extending them? Are there any other ways?Perhaps no? This is the only way? I am sorry if this seems like a trivial question but i get stuck on this. Thank you.