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首页> 外文期刊>Journal of algebra and its applications >Geometry of balanced and absorbing subsets of topological modules
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Geometry of balanced and absorbing subsets of topological modules

机译：拓扑模块平衡和吸收子集的几何形状

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We define the concepts of balanced set and absorbing set in modules over topological rings, which coincide with the usual concepts when restricting to topological vector spaces. We show that in a topological module over an absolute semi-valued ring whose invertibles approach 0, every neighborhood of 0 is absorbing. We also introduce the concept of total closed unit neighborhood of zero (total closed unit) and prove that the only total closed unit of the quaternions H is its closed unit ball B-H. On the other hand, we also prove that if A is an absolute semi-valued unital real algebra, then its closed unit ball B-A is a total closed unit. Finally, we study the geometry of modules via the extreme points and the internal points, showing that no internal point can be an extreme point and that absorbance is equivalent to having 0 as an internal point.
机译：我们在拓扑圈上定义模块中的平衡集和吸收集的概念，这在限制拓扑矢量空间时与通常的概念一致。 我们展示在拓扑模块中，通过绝对的半值环，其偏差偏离0，0的每个邻域都是吸收。 我们还介绍了零（总封闭单元）的总闭合单元附近的概念，并证明了四元数H的唯一封闭单元是其封闭的单位球B-H。 另一方面，我们还证明，如果A是绝对半值的Unital Real代数，那么它的闭合单元球B-A是一个完全封闭的单元。 最后，我们通过极端点和内部点研究模块的几何形状，表明没有内部点可以是极端点，并且吸光度相当于将0作为内部点。

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