[def-lkb]

> spaces whose distance measures obey the triangle inequality

That would be a metric space, and a distance obey the triangle inequality by definition. The element of the space are otherwise quite arbitrary.

Unfortunately, Normed spaces are a subset of metric spaces which are much less general (in particular they have to be vector spaces).

[macleginn]

You are right, I wantonly omitted some of the important properties. Cf. the response of one of the authors in another comment on how their method tackles general metric spaces.