Just learning about space filling curves and it has made me question the definition of dimensions. The standard explanation is that the dimension is the minimum number och values needed to represent something, but if, by use of space filling curves one can map any set of values to one single value, in what sense do dimensions exist?
Or perhaps more correctly, what properties can not carry over when you map something to a lower dimension?
Note: I'm not questioning the usefulness of representing something with several dimensions
My level of mathematics: 1 year in to an undergraduate math degree