发表机构
Universidad de Chile; Center for Mathematical Modeling (CNRS IRL2807)（智利大学; 数学建模中心（法国国家科学研究中心第2807联合研究国际单位））
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提供平铺空间紧致性定理的自包含完整证明，填补文献空白，并详细解释常被省略的论证，以促进该基本结果的理解。
AI 中文摘要
配备标准平铺度量的平铺空间的紧致性是一个经典结果。然而，据我们所知，文献中似乎没有将所有相关细节明确化的完整证明。本注记旨在给出紧致性定理的一个自包含且具有教学性的处理，提供完整证明并仔细解释通常被省略的论证。我们希望这一阐述能提供一个有用的参考，并有助于更清晰、更易理解地认识平铺理论中这一基本结果。
英文摘要
The compactness of the tiling space and the continuity of the action of the Euclidean space by translation, as well as the minimality of this action for repetitive tilings, are among the most frequently mentioned foundational facts in the dynamical theory of aperiodic order. Nonetheless, despite their classical status, a comprehensive treatise with complete and detailed proofs, to the best of our knowledge, is not available in the literature: existing arguments are typically sketched, deferred to other sources, or rely on unstated results or hypotheses. The purpose of this manuscript is to give a self-contained and pedagogical treatment of these foundations, providing complete and carefully explained proofs. We hope that this exposition will provide a useful reference and contribute to a clearer and more accessible understanding of the fundamentals of the theory of tiling dynamical systems.
CommentsReferences added, minor typos corrected and changes to the presentation
