Topological Lifting of Mundici Equivalence and Di Nola--Lettieri Equivalence
Year: 2026
Type: preprint
Abstract: Notice: The PDF in this version (v2) was uploaded in error.Please refer to the corrected version (v3):https://doi.org/10.5281/zenodo.23993564. We prove that summability characterises precisely when a topological MV-algebra can be realized as the unit interval of a lattice-ordered topological abelian group, thereby providing a topological lifting of both Mundici equivalence and Di Nola--Lettieri equivalence. Applications include a Birkhoff--Kakutani-type metrisation theorem, a second-countability criterion, and a topological extension of a key continuity lemma from the proof theory of first-order {\L}ukasiewicz logic---following Baaz--Metcalfe's hypersequent approach to approximate completenesss---and provides an $A$-valued topological semantics for the approximate strong completeness of $\mathbf{G}\text{{\L}}\forall$, where $A$ ranges over summable topological MV-algebras.
Authors: Jia, Yanqiao, Yang, Yichuan
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225341678