We present some lifting theorems for continuous order-preserving functions on locally and σ -compact Hausdorff preordered topological spaces. In particular, we show that a preorder on a locally and σ -compact Hausdorff topological space has a continuous multi-utility representation if, and only if, for every compact subspace, every continuous order-preserving function can be lifted to the entire space. Such a characterization is also presented by introducing a lifting property of ≾-C-compatible continuous order-preserving functions on closed subspaces. The assumption of paracompactness is also used in connection to lifting conditions.

Lifting Theorems for Continuous Order-Preserving Functions and Continuous Multi-Utility

Gianni Bosi
;
2023-01-01

Abstract

We present some lifting theorems for continuous order-preserving functions on locally and σ -compact Hausdorff preordered topological spaces. In particular, we show that a preorder on a locally and σ -compact Hausdorff topological space has a continuous multi-utility representation if, and only if, for every compact subspace, every continuous order-preserving function can be lifted to the entire space. Such a characterization is also presented by introducing a lifting property of ≾-C-compatible continuous order-preserving functions on closed subspaces. The assumption of paracompactness is also used in connection to lifting conditions.
2023
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11368/3039060
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