Motivated by the concept of lattice-bornological vector spaces of J. Paseka, S. Solovyov and M. Stehlík, which extends bornological vector spaces to the fuzzy setting over a complete lattice, this paper continues to study the theory of L-bornological vector spaces. The specific description of L-bornological vector spaces is presented, some properties of Lowen functors between the category of bornological vector spaces and the category of L-bornological vector spaces are discussed. In addition, the notions and some properties of L-Mackey convergence and separation in L-bornological vector spaces are showed. The equivalent characterization of separation in L-bornological vector spaces in terms of L-Mackey convergence is obtained in particular.

中文翻译：

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诱导的L-出生学向量空间和L-Mackey收敛1

受到J.Paseka，S.Solovyov和M.Stehlík的晶格-出生学矢量空间概念的启发，该理论将出生学矢量空间扩展到整个晶格上的模糊设定，本文继续研究L-胎教矢量空间理论。介绍了L-胎教向量空间的具体描述，讨论了L-函子在胎教向量空间类别与L-胎教向量空间类别之间的一些性质。此外，还展示了L-年龄学向量空间中L-Mackey收敛和分离的概念和一些性质。特别地，获得了根据L-Mackey收敛的L-出生学向量空间中的分离的等效特征。