New characterizations of completely useful topologies in mathematical utility theory

• Tác giả: Gianni Bosi, Roberto Daris, Gabriele Sbaiz
• Ngôn ngữ: eng
• Ký hiệu phân loại: 514.2 Algebraic topology
• Thông tin xuất bản: 2024
• Bộ sưu tập: Báo, Tạp chí
• ID: 201818

Tóm tắt

Comment: Title changedLet $X$ be an arbitrary set. Then a topology $t$ on $X$ is said to be completely useful if every upper semicontinuous linear (total) preorder $\precsim$ on $X$ can be represented by an upper semicontinuous real-valued order preserving function. In this paper, appealing, simple and new characterizations of completely useful topologies will be proved, therefore clarifying the structure of such topologies.