论文标题
通过点对函数诱导的指标和准对象
Metrics and quasimetrics induced by point pair function
论文作者
论文摘要
我们研究子域中的点对函数$ g $ of $ \ mathbb {r}^n $。我们证明，对于每个域，$ g \ subsetneq \ mathbb {r}^n $，此函数是一个准米，其常数小于或等于$ \ sqrt {5} \ slash2 $。此外，我们证明它是域中的度量，$ g = \ mathbb {r}^n \ setMinus \ {0 \} $，带有$ n \ geq1 $。我们还根据任意常数$α> 0 $考虑了点对函数的通用版本，并在某些域中显示，这些概括是指标，并且仅当$α\ leq12 $。
We study the point pair function in subdomains $G$ of $\mathbb{R}^n$. We prove that, for every domain $G\subsetneq\mathbb{R}^n$, the this function is a quasi-metric with the constant less than or equal to $\sqrt{5}\slash2$. Moreover, we show that it is a metric in the domain $G=\mathbb{R}^n\setminus\{0\}$ with $n\geq1$. We also consider generalized versions of the point pair function, depending on an arbitrary constant $α>0$, and show that in some domains these generalizations are metrics if and only if $α\leq12$.
