Topology Atlas
Document # ppae-01

## 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.

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Copyright © 2002
Charles University and
Topology Atlas.
Published April 2002.