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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 rangespaces. Specifically, we assume that the range space has a sequential webstructure and do not require that it be metrizable, nor strictly barrelled, andthe range space need not even be barrelled. Distinguishing examples areprovided that include natural constructions of range spaces connected withapplications, such as the space of distributions having their wavefront sets ina specified closed cone. The same and other examples could also serve as domainspaces for the closed graph theorem of Valdivia, revealing a much widercollection of domain spaces that can be used in that result.

Valdivia's lifting theorem for non-metrizable spaces. Preprint