I’d feel better if I knew what I meant by “dimension” here though; it’s not a vector space.
The number of parameters you need to label each element (provided the labelling is a continuous function, otherwise you can label points of R^2 with a single parameter e.g. (3.1415..., 2.7182...) → 32.174118...)
The number of parameters you need to label each element (provided the labelling is a continuous function, otherwise you can label points of R^2 with a single parameter e.g. (3.1415..., 2.7182...) → 32.174118...)
To make this precise, you need the idea of “charts” and “atlases” that witzvo references.