Existence of a sublinear continuous order-preserving function for a noncomplete preorder on a topological vector space by Gianni Bosi and Magali E. Zuanon

Toposym

Existence of a sublinear continuous order-preserving function for a noncomplete preorder on a topological vector space

Gianni Bosi and Magalí E. Zuanon

Proceedings of the Ninth Prague Topological Symposium (2001) pp. 1-8

We characterize the existence of a nonnegative, sublinear and continuous order-preserving function for a not necessarily complete preorder on a real convex cone in an arbitrary topological real vector space. As a corollary of the main result, we present necessary and sufficient conditions for the existence of such an order-preserving function for a complete preorder.

Mathematics Subject Classification. 28B15 06A06 91B16.
Keywords. Topological vector space; preordered real cone; sublinear order-preserving function; decreasing scale.

Document formats: AtlasImage (for online previewing); LaTeX 24.6 Kb; DVI 36.6 Kb; PostScript 157.4 Kb; gzipped PostScript 62.8 Kb; PDF 184.4 Kb
arXiv: math.GN/0204101
Metadata: Citation; Reference list in BibTeX

Comments. This article is in final form.