Sure, but did we need continuity? Also, if you want to be awkward, you can get around this by using the discrete topology, I don't think we needed the metric structure of R^n.
> Sure, but did we need continuity? Also, if you want to be awkward, you can get around this by using the discrete topology
This is indeed possible - but this is clearly not the topology that "ordinary people" and physicists mean when talking about continuity of functions from R^n to R^m.
This is indeed possible - but this is clearly not the topology that "ordinary people" and physicists mean when talking about continuity of functions from R^n to R^m.