对合量子格与量子格赋值的对合拓扑空间
Involutive quantales and quantale-enriched involutive topological spaces
AI总结：
本文扩展量子格赋值拓扑空间以包含对合，通过量子框架平衡拓扑化单位$C^*$-代数谱，并识别纯态子空间为强Hausdorff分离的对合空间。
摘要：
本文对对合量子格进行了全面分析，特别关注量子框架。我们将量子格赋值的拓扑空间的公理基础扩展，以包含反同态对合下的闭包性，从而通过量子框架的概念，实现对单位$C^*$-代数的谱的平衡拓扑化，涵盖闭右理想和闭左理想。具体而言，纯态的某些子空间被识别为强Hausdorff分离的量子格赋值的对合拓扑空间。
英文摘要：
In this paper, we provide a comprehensive analysis of involutive quantales, with a particular focus on quantic frames. We extend the axiomatic foundations of quantale-enriched topological spaces to include closure under the anti-homomorphic involution, facilitating a balanced topologization of the spectrum of unital $C^*$-algebras that encompasses both closed right and left ideals through the concept of quantic frames. Specifically, certain subspaces of pure states are identified as strongly Hausdorff separated quantale-enriched involutive topological spaces.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
