Complex sentence: In dimension one this is the real line; in dimension two it is the Cartesian plane; and in higher dimensions it is a coordinate space with three or more real number coordinates--in short, an "n"-dimensional real coordinate space.
Split into simpler sentences: In dimension one this is the real line; in dimension two it is the Cartesian plane; and in higher dimensions it is a coordinate space with three or more real number coordinates. In short, an "n"-dimensional real coordinate space.