The vector lattice structure on the Isbell-convex hull of an asymmetrically normed real vector space

An explicit description of the algebraic and vector lattice operations on the Isbell-convex hull of an asymmetrically normed real vector space is provided. Connections between the concepts of Isbell-convexity, injectivity and Dedekind-completeness of asymmetrically normed real vector spaces are also considered.