论文标题
Valdivia的提升定理，用于不可弥补的空间。预印本
Valdivia's lifting theorem for non-metrizable spaces. Preprint
论文作者
论文摘要
Valdivia关于（PRE）紧凑型组的提升定理和收敛（分别是Cauchy）序列从准（LB）空间到可迁移的，严格的桶形空间的序列扩展到严格的范围更大的范围集合。具体而言，我们假设范围空间具有连续的Web结构，并且不需要它是可倾斜的，也不严格桶形的，并且范围空间甚至不需要桶。提供了区分示例，其中包括与应用程序连接的范围空间的自然结构，例如在指定的封闭锥体中具有波前置的分布空间。相同的示例也可以用作瓦尔迪维亚封闭图定理的域空间，揭示了可以在该结果中使用的域空间的较宽集合。
The lifting theorem of Valdivia concerning (pre) compact sets and convergent (respectively, Cauchy) sequences from a quasi-(LB) space to a metrizable, strictly barrelled space is extended to a strictly larger collection of range spaces. Specifically, we assume that the range space has a sequential web structure and do not require that it be metrizable, nor strictly barrelled, and the range space need not even be barrelled. Distinguishing examples are provided that include natural constructions of range spaces connected with applications, such as the space of distributions having their wavefront sets in a specified closed cone. The same and other examples could also serve as domain spaces for the closed graph theorem of Valdivia, revealing a much wider collection of domain spaces that can be used in that result.
