← 研踪 PaperTrailarXiv:2603.14955 · v4
Convex algebras on an interval with semicontinuous monotone operations
首次提交 2026-03-16 16:10
版本更新 2026-11-03 03:09
雷达观测 2026-11-04 23:41
摘要
In a recent work of Matteo Mio on compact quantitative equational theories (here compact means that all its consequences are derivable by means of finite proofs) convex algebras on the carrier set [0,1] whose operations are monotone and satisfy certain semicontinuity properties occurred. We fully classify those algebraic structures by giving an explicit construction of all possible convex operations on [0,1] possessing the mentioned properties. Our result thus describes exactly the range of theories to which Mio's theorem applies.
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v4 · 2026-11-03 03:09 · 最新观测版本
Convex algebras on an interval with semicontinuous monotone operations
In a recent work of Matteo Mio on compact quantitative equational theories (here compact means that all its consequences are derivable by means of finite proofs) convex algebras on the carrier set [0,1] whose operations are monotone and satisfy certain semicontinuity properties occurred. We fully classify those algebraic structures by giving an explicit construction of all possible convex operations on [0,1] possessing the mentioned properties. Our result thus describes exactly the range of theories to which Mio's theorem applies.
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