Net-Compact Hausdorff Topologies and Continuous Multi-Utility Representations for Closed Preorders
In this paper, we deal with continuous multi-utility representations for closed preorders. We introduce the definition of a <i>net-compact topology</i>, which generalizes the concept of a sequentially compact topology. Indeed, a sequentially compact and first countable topological space...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-03-01
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| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/14/3/188 |
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| Summary: | In this paper, we deal with continuous multi-utility representations for closed preorders. We introduce the definition of a <i>net-compact topology</i>, which generalizes the concept of a sequentially compact topology. Indeed, a sequentially compact and first countable topological space is net-compact. First, we show that if every closed preorder on a net-compact Hausdorff topological space has a continuous multi-utility representation, then the topology is normal. Second, we prove that every closed preorder on a normal and net-compact Hausdorff topological space admits a continuous multi-utility representation. |
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| ISSN: | 2075-1680 |