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
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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.File | Dimensione | Formato | |
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