Let [Formula: see text] be an expansion of either an ordered field [Formula: see text], or a valued field [Formula: see text]. Given a definable set [Formula: see text] let [Formula: see text] be the ring of continuous definable functions from [Formula: see text] to [Formula: see text]. Under very mild assumptions on the geometry of [Formula: see text] and on the structure [Formula: see text], in particular when [Formula: see text] is [Formula: see text]-minimal or [Formula: see text]-minimal, or an expansion of a local field, we prove that the ring of integers [Formula: see text] is interpretable in [Formula: see text]. If [Formula: see text] is [Formula: see text]-minimal and [Formula: see text] is definably connected of pure dimension [Formula: see text], then [Formula: see text] defines the subring [Formula: see text]. If [Formula: see text] is [Formula: see text]-minimal and [Formula: see text] has no isolated points, then there is a discrete ring [Formula: see text] contained in [Formula: see text] and naturally isomorphic to [Formula: see text], such that the ring of functions [Formula: see text] which take values in [Formula: see text] is definable in [Formula: see text].

中文翻译：

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在拓扑域上的连续可定义函数环中定义整数值函数

令 [Formula: see text] 是有序字段 [Formula: see text] 或有值字段 [Formula: see text] 的扩展。给定一个可定义的集合 [Formula: see text] 让 [Formula: see text] 是从 [Formula: see text] 到 [Formula: see text] 的连续可定义函数的环。在对[公式：见文本]的几何和结构[公式：见文本]的非常温和的假设下，特别是当[公式：见文本]是[公式：见文本]-minimal或[公式：见文本]时-minimal 或局部域的扩展，我们证明整数环 [Formula: see text] 在 [Formula: see text] 中是可解释的。如果 [Formula: see text] 是 [Formula: see text]-minimal 且 [Formula: see text] 可定义为纯维度 [Formula: see text] 连接，则 [Formula: see text] 定义子环 [Formula: see text]文本]。如果 [公式：