Maximal elements of preorders from countable continuous multi-utilities

Key Points

• Investigate conditions on topologies for countable continuous multi-utility representations of closed preorders and their maximal elements.
• Analyzed topological conditions under which closed preorders allow multi-utility representations.
• Compared these conditions to prior known criteria for continuous utility representations.
• Applied findings to establish the existence of maximal elements in specific topological frameworks.
• Demonstrated that specific topological conditions facilitate countable continuous multi-utility representation of closed preorders.
• Identified frameworks in compact metrizable spaces wherein maximal elements are guaranteed to exist.
• Showed comparative effectiveness of new conditions against existing ones for total preorders.