Abstract We consider Lipschitz maps with values in quasi-metric spaces and extend such maps to finitely many points. We prove that in this context every 1-Lipschitz map admits an extension such that its Lipschitz constant is bounded from above by the number of added points plus one. Moreover, we prove that if the source space is a Hilbert space and the target space is a Banach space, then there exists an extension such that its Lipschitz constant is bounded from above by the square root of the total of added points plus one. We discuss applications to metric transforms.

中文翻译：

---

有限多点的 Lipschitz 扩展

摘要 我们考虑在拟度量空间中具有值的 Lipschitz 映射并将此类映射扩展到有限多个点。我们证明，在这种情况下，每个 1-Lipschitz 映射都允许扩展，使得它的 Lipschitz 常数从上方开始由添加点的数量加 1 限定。此外，我们证明如果源空间是 Hilbert 空间而目标空间是 Banach 空间，那么存在一个扩展使得它的 Lipschitz 常数从上方以相加点总数加 1 的平方根为界。我们讨论了度量转换的应用。