So I had a doubt. We can also define an "epsilon-delta limit" definition for any metric and not just the cartesian metric, right? And in all those cases, I will obtain the same limit, right?
@RyanUnger I actually don't know a lot about that - most CFT I know is 2d (worldsheet theories in string theory) and beyond the buzzwords I don't have a good understanding of what goes on in AdS/CFT specifically
@FakeMod All norms on finite-dimensional vector spaces are equivalent (generate the same topology and hence the same notions of convergence), but not all metrics are.
@ACuriousMind @NiharKarve What if I only consider those metrics which are continuous, i.e. not taxicab metric? Could I then obtain the same limit from all of them?
BTW @NiharKarve, if you don't mind sharing, where do you study?
@FakeMod A "non-continuous metric" does not make any sense - in a metric space, you're using the metric to define the topology, and you can show that every metric is continuous in the topology it induces
