We present a sufficient and necessary condition for a function module space $X$ to have the approximate hyperplane series property (AHSP). As a consequence, we have that the space ${\mathcal{C}}_{0}(L,E)$ of bounded and continuous $E$-valued mappings defined on the locally compact Hausdorff space $L$ has AHSP if and only if $E$ has AHSP.

中文翻译：

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在具有近似超平面系列性质的功能模块上

我们提出了功能模块空间的充分必要条件$X$具有近似超平面级数特性（AHSP）。因此，我们有空间${\mathcal{C}}_{0}(L,E)$有界和连续的$E$在局部紧致 Hausdorff 空间上定义的值映射$L$当且仅当有 AHSP$E$有AHSP。