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Diagonal conditions for lattice-valued uniform convergence spaces

机译:格值均匀收敛空间的对角条件

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摘要

We define diagonal conditions for lattice-valued uniform convergence spaces and show that these conditions are preserved under initial constructions. Further, the forgetful functor from the category of stratified lattice-valued uniform convergence spaces into the category of stratified lattice-valued limit spaces maps these conditions to corresponding conditions. We especially define uniform regularity and characterize this condition by certain closures of lattice-valued filters. As an application we generalize an extension theorem for uniformly continuous mappings.
机译:我们为晶格值均匀收敛空间定义了对角条件,并表明这些条件在初始构造下得以保留。此外,从分层晶格值均匀收敛空间的类别到分层晶格值极限空间的类别的健忘函子将这些条件映射到相应条件。我们特别定义统一的规则性,并通过某些晶格值过滤器的闭合来表征这种情况。作为应用程序,我们推广了一致连续映射的扩展定理。

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