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

Autor:	Gianni Bosi, Magalì Zuanon
Jazyk:	angličtina
Rok vydání:	2023
Předmět:	order-preserving function locally compact space continuous multi-utility representation Mathematics QA1-939
Zdroj:	Axioms, Vol 12, Iss 2, p 123 (2023)
Druh dokumentu:	article
ISSN:	2075-1680
DOI:	10.3390/axioms12020123
Popis:	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.
Databáze:	Directory of Open Access Journals
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