论文标题
在非架构的功能分析中的某些紧凑型特性
Some compact-like properties in non-archimedean functional analysis
论文作者
论文摘要
首先，我们定义了类似于局部紧凑型性或C-compactness的一些概念，并研究了这些概念与原始概念之间的关系。结果，当局部紧凑型电场的球场完成时，我们发现局部紧凑型性的表征。此外，从最低原则的角度来看，我们在适当的条件下为C-CORPACTS提供了必要的条件。其次，我们尝试采用一种新的方法来实现不完整的本地紧凑型，这给我们带来了与以前不同的看法。第三，我们研究了非Archimedean Goldstine定理和Eberlein-Smulian定理。因此，如果系数字段已完成，我们将获得与经典的结果完全不同的结果。最后，我们通过使用表面性给出了有关封闭范围定理的新结果。
First, we define some concepts similar to the local compactoidity or the c-compactness, and study relationships between these concepts and the original ones. As a result, we find a characterization of the local compactoidity when its coefficient field is spherically complete. Moreover, from the point of view of the minimum principle, we give a necessary and sufficient condition for the c-compactness under a suitable condition. Secondly, we try a new approach to a non-complete local compactoid, which gives us a different perspective than before. Thirdly, we study the non-archimedean Goldstine theorem and Eberlein-Smulian theorem. Consequently, if the coefficient field is spherically complete, we get results completely different from the classical ones. Finally, we give a new result about the closed range theorem by using epicompactness.
