1. Euclidean sets

Geometry is, historically, the branch of mathematics that studies figures in the plane and in space.

The generic term “object,” which has primarily an applied connotation, is traditionally used in geometry to refer to a planar object—that is, a subset of the Euclidean plane ${ℝ}_2^2$ (historically referred to as a “figure” or, more precisely, a “planar figure”) or a spatial object, that is, a subset of Euclidean space ${ℝ}_2^3$ (historically referred to as a “solid” or “spatial figure”).

In other scientific fields, the term "object" refers to a cell (in biology),...