AI 中文总结
针对比固定指数更快趋于零的正序列，在实数加法群上构造了介于最小与通常拓扑之间的豪斯多夫拓扑向量群拓扑，并给出示例及比较准则。
AI 中文摘要
对于每一个比任意固定指数更快趋于零的正序列，我们在实数加法群上构造了一个豪斯多夫拓扑向量群拓扑。该拓扑严格介于最小豪斯多夫拓扑向量群拓扑与通常拓扑之间。我们通过阶乘幂、二次指数衰减以及除以二次指数的素数幂次来示例说明该构造。我们还记录了一个用于比较两个此类拓扑的有限标量覆盖准则。
英文摘要
For every positive sequence that tends to zero faster than every fixed exponential, we construct a Hausdorff topological Vector Group topology on the additive group of real numbers. It lies strictly between the minimal Hausdorff topological Vector Group topology and the usual topology. The construction is illustrated by factorial powers, quadratic exponential decay, and prime radicals divided by a quadratic exponential. We also record a finite scalar covering criterion for comparing two such topologies.
Comments9 pages, no figures. Complete proof and three examples
