We study the problem of extending continuous quasiconvex real-valued functions from a subspace of a real normed linear space. Our results are essentially finite-dimensional and are based on a technical lemma which permits to “extend” a nested family of open convex subsets of a given subspace to a nested family of open convex sets in the whole space, in such a way that certain topological conditions are satisfied.

中文翻译：

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关于连续拟凸函数的推广

我们研究从实范数线性空间的子空间扩展连续拟凸实值函数的问题。我们的结果本质上是有限维的，并且基于一个技术引理，该引理允许将给定子空间的开凸子集的嵌套族“扩展”到整个空间中的开凸集的嵌套族，使得某些满足拓扑条件。