论文标题
Lebesgue编号和总界限
Lebesgue Number and Total Boundedness
论文作者
论文摘要
获得Lebesgue数量引理的概括。事实证明，如果每个可计数的无限本地有限的开放式封面$ x $都有lebesgue号码，则$ x $完全有限。引入了指标空间的属性，即连接性和Menger凸度的概括。可以观察到，对于该引入的特性以及可链式的度量空间，Atsujiness和Compacts与度量空间相当。
A generalization of the Lebesgue number lemma is obtained. It is proved that, if each countably infinite locally finite open cover of a chainable metric space $X$ has a Lebesgue number, then $X$ is totally bounded. A property of metric spaces which is a generalization of connectedness and Menger convexity is introduced. It is observed that Atsujiness and compactness are equivalent for a metric space with this introduced property as well as for a chainable metric space.
