Normally preordered spaces and utilities

Abstract

In applications it is useful to know whether a topological preordered space is normally preordered. It is proved that every $k_{\omega }$-space equipped with a closed preorder is a normally preordered space. Furthermore, it is proved that second countable regularly preordered spaces are perfectly normally preordered and admit a countable utility representation.

17 pages, 1 figure. v2 contains a second proof to the main theorem with respect to the published version. The last section of v1 is not present in v2. It will be included in a different work

References in corpus (2)

• Normally preordered spaces and utilities
• Time functions as utilities

Cited by in corpus (13)

• Normally preordered spaces and utilities
• Convexity and quasi-uniformizability of closed preordered spaces
• Partial representations of orderings
• A topological study for the existence of lower-semicontinuous Richter-Peleg multi-utilities
• Quasi-pseudo-metrization of topological preordered spaces
• Representing preorders with injective monotones
• Gluing of Lorentzian length spaces and the causal ladder
• Further observations on the definition of global hyperbolicity under low regularity
• On the regularity of Cauchy hypersurfaces and temporal functions in closed cone structures
• The representation of spacetime through time functions
• Characterization of the existence of semicontinuous Richter-Peleg multi-utility representations
• Compactification of closed preordered spaces
• Topological conditions for the representation of preorders by continuous utilities