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This randomized trial explores conditions for maximal elements in preorders on compact metrizable spaces, indicating significant theoretical implications.
We present conditions on a topology, under which every closed preorder admits a countable continuous multi-utility representation. We compare such topological conditions with other existing conditions, which guarantee the existence of continuous utility representations of all continuous total preorders. We apply our results to the existence of maximal elements of preorders on compact metrizable topological spaces.
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Bosi et al. (2026) studied this question.
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