光滑分布是有限生成的
Smooth distributions are finitely generated
AI总结：
本文证明光滑流形上变维数切子丛（光滑分布）可由有限个向量场生成，并指出其截面模不必有限生成，结果推广至任意向量丛。
摘要：
光滑流形切丛内变维数的子丛称为光滑分布，如果它是光滑向量场族的逐点张成。我们证明所有这样的分布都是有限生成的，即该族可以取为有限集合。进一步，我们证明此类分布的光滑截面空间作为光滑函数上的模不必是有限生成的。我们的结果在更一般的情况下成立，其中切丛可以被任意向量丛替换。论文当前版本已将2026年9月21日的更正并入原文。
英文摘要：
A subbundle of variable dimension inside the tangent bundle of a smooth manifold is called a smooth distribution if it is the pointwise span of a family of smooth vector fields. We prove that all such distributions are finitely generated, meaning that the family may be taken to be a finite collection. Further, we show that the space of smooth sections of such distributions need not be finitely generated as a module over the smooth functions. Our results are valid in greater generality, where the tangent bundle may be replaced by an arbitrary vector bundle. The current version of the paper incorporates the corrigendum of 9-21-2026 into the original.
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。
