nLab
finite-dimensional space

Given a notion of space and a notion of dimension assigning a cardinal number or ordinal number to each space (or at least to some of them), a space is finite-dimensional if this dimension exists as a natural number. Whether one is talking about vector spaces, topological spaces, manifolds, or whatever, finite-dimensional spaces tend to have nicer properties than arbitrary spaces (such as infinite-dimensional manifolds).

Spaces with fractal dimension may also be considered finite-dimensional, but that's not usually what people are talking about when they say ‘finite-dimensional space’.

Created on October 27, 2013 at 17:24:01. See the history of this page for a list of all contributions to it.