论文标题
瓶颈距离的基本度量几何形状
Basic Metric Geometry of the Bottleneck Distance
论文作者
论文摘要
给定公制对$（x，a）$，即公制空间$ x $和一个杰出的封闭套件$ a \ subset x $，一个人可以以功能方式构造一个尖的伪级$ \ MATHCAL {d} _ \ intcal {d} _ \ infty（x，x，x，a）$持久性图。我们研究了空间的基本度量属性$ \ mathcal {d} _ \ infty（x，a）$，并获得其METRINISINES，完整性，可分离性和地理位置的特征。
Given a metric pair $(X,A)$, i.e. a metric space $X$ and a distinguished closed set $A \subset X$, one may construct in a functorial way a pointed pseudometric space $\mathcal{D}_\infty(X,A)$ of persistence diagrams equipped with the bottleneck distance. We investigate the basic metric properties of the spaces $\mathcal{D}_\infty(X,A)$ and obtain characterizations of their metrizability, completeness, separability, and geodesicity.
