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<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(C^*\)</EquationSource> </InlineEquation>-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, involutive quantale-enriched topological spaces.</p>

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Involutive Quantales and Quantale-Enriched Involutive Topological Spaces

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年12月20日

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  • Javier Gutiérrez García,
  • Ulrich Höhle

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, involutive quantale-enriched topological spaces.