geometric dimension <geometry, topology>
largest number n such that each point in a set of points can be associated with a subset that has that point in its interior and is topologically isomorphic to 𝔼n, Euclidean n-space
Note to entry: Curves, because they are continuous images of a portion of the real line, have geometric dimension 1. Surfaces cannot always be mapped to `RR^2` in their entirety, but around each point position, a small neighborhood can be found that resembles (under continuous functions) the interior of the unit circle in `RR^2`, and are therefore 2-dimensional. In this document, most surfaces (instances of Surface) are mapped to portions of `RR^2` by their defining interpolation mechanisms.
ORIGIN: ISO/TC 211 Glossary of Terms - English (last updated: 2020-06-02)