Buskes, GerardSchwanke, Christopher2017-04-052017-04-052016Buskes, G. & Schwanke, C. 2016. Functional completions of Archimedean vector lattices. Algebra universalis, 76(1):53-69. [https://doi.org/10.1007/s00012-016-0386-z]0002-52401420-8911 (Online)http://hdl.handle.net/10394/21084https://doi.org/10.1007/s00012-016-0386-zhttps://link.springer.com/article/10.1007%2Fs00012-016-0386-zWe study completions of Archimedean vector lattices relative to any nonempty set of positively homogeneous functions on finite-dimensional real vector spaces. Examples of such completions include square mean closed and geometric mean closed vector lattices, amongst others. These functional completions also lead to a universal definition of the complexification of any Archimedean vector lattice and a theory of tensor products and powers of complex vector lattices in a companion paperenVector latticesFunctional calculusFunctional completionsConvex functionsArticle