等价度量和紧化
Equivalent metrics and compactifications
摘要：
设（X，d）是度量空间，m \in X.假设n：X \times X \to \mathbold{R}是非负对称函数。我们在X上定义一个度量d^{m，m}，它等价于d。如果d^{X，m}是完全有界的，则它的完备化是（X，d）的紧化。作为例子，我们构造了（\mathhbold{R}^s，d_E）的两个紧化，其中d_E是欧氏度量，s \geq 2.
英文摘要：
Let (X,d) be a metric space and m\in X. Suppose that ϕ:X\times X\to\mathbold{R} is a nonnegative symmetric function. We define a metric d^{ϕ,m} on X which is equivalent to d. If d^{ϕ,m} is totally bounded, its completion is a compactification of (X,d). As examples, we construct two compactifications of (\mathhbold{R}^s,d_E), where d_E is the Euclidean metric and s\geq 2.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
