一句话：弱化 Spreen 编号基表示条件，统一多种表示，并用强/形式包含关系保证 Cauchy 一致与多表示兼容。
本文重新审视 Spreen 提出的、与带强包含关系的编号基相关联的表示概念。作者放松其要求，将 Grubba、Weihrauch、Schröder 等经典表示纳入为特例。核心方法是用子基编号和形式包含关系定义多表示，并分析不同包含关系对表示行为的影响。结果表明：采用合适的强包含关系时，可计算度量空间视为拓扑空间所诱导的表示与 Cauchy 表示一致；采用形式包含关系时，在集合及其子集上定义的多表示彼此兼容，即包含映射可计算。此外，新定义在等价基更换下更具稳健性。
We revisit Dieter Spreen's notion of a representation associated to a numbered basis equipped with a strong inclusion relation. We show that by relaxing his requirements, we obtain different classically considered representations as subcases, including representations considered by Grubba, Weihrauch and Schröder. We show that the use of an appropriate strong inclusion relation guarantees that the representation associated to a computable metric space seen as a topological space always coincides with the Cauchy representation. We also show how the use of a formal inclusion relation guarantees that when defining multi-representations on a set and on one of its subsets, the obtained multi-representations will be compatible, i.e. inclusion will be a computable map. The proposed definitions are also more robust under change of equivalent bases.
DOI 原文 · arXiv · PDF（开放获取） · DBLP
@article{Rauzy25,
title = {Multi-representation associated to the numbering of a subbasis and formal inclusion relations},
author = {Emmanuel Rauzy},
journal = {Logical Methods in Computer Science},
volume = {Volume 21, Issue 3},
year = {2025},
doi = {10.46298/lmcs-21(3:29)2025}
}