Lines and Planes in a Metrical Space

§ 1. “Stretches” joining Points in a Metrical Space.If x, y, z are any points in a metrical space, then by definitionRegarding x and y as fixed, we may define the set of points z for whichas the “stretch joining the points xy” or more shortly the stretch xy*. Then for points z not on the stretch,The stretch xy always contains the points x and y themselves, which we may call the “end-points” of the stretch. In particular cases, it may contain no other points: e.g. with the function δ0(x, y) = 1 when xǂy, each stretch contains only its end-points †.