x\leq 0.} An Archimedean (pre)ordered vector space is a (pre)ordered vector space whose order is Archimedean. A preordered vector space X {\displaystyle...

an ordered vector space or partially ordered vector space is a vector space equipped with a partial order that is compatible with the vector space operations...

. – Alternative decimal expansion of 1 Archimedean ordered vector space – A binary relation on a vector space Construction of the real numbers "Math 2050C...

analysis and order theory, an ordered topological vector space, also called an ordered TVS, is a topological vector space (TVS) X that has a partial order...

Riesz space, lattice-ordered vector space or vector lattice is a partially ordered vector space where the order structure is a lattice. Riesz spaces are...

order An ordered vector space is a partially ordered group A Riesz space is a lattice-ordered group A typical example of a partially ordered group is...

This property implies that the field is Archimedean. Vector spaces (particularly, n-spaces) over an ordered field exhibit some special properties and...

order topology of an ordered vector space ( X , ≤ ) {\displaystyle (X,\leq )} is the finest locally convex topological vector space (TVS) topology on X...

formalism of vector spaces, with the work of Hermann Grassmann and Giuseppe Peano, the latter of whom first gave the modern definition of vector spaces as an...

considered as a vector space over R {\displaystyle \mathbb {R} } then it is an Archimedean ordered vector space. Let A be an ordered algebra with unit...