A CANONICAL PARAMETERIZATION OF PATHS IN R
A CANONICAL PARAMETERIZATION OF PATHS IN R
复制标题
R 中路径的规范参数化
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
E. Tymchatyn
中科院分区：
文献类型：
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作者：
L. Oversteegen;E. Tymchatyn
对于Rn中足够驯服的路径，欧几里得长度提供了路径长度的规范参数化。在本文中，我们提供了这样的参数化的所有连续路径。这种参数化是基于路径长度的另一种概念，我们称之为len。像欧几里德路长一样，len在Rn的等距下是不变的，关于子路是单调的，并且对于Rn中的任何两点，它们之间的直线段具有最小的len长度。与欧几里德路径长度不同，任何路径的透镜长度都是定义的（即，有限），并且透镜相对于路径之间的均匀距离是连续的。我们使用这个概念来获得这些家庭的道路，可以重新参数化是等度连续的或紧的特征。最后，我们使用这个参数化，以获得一个典型的同胚之间的某些家庭的弧。
For sufficiently tame paths in Rn, Euclidean length provides a canonical parametrization of a path by length. In this paper we provide such a parametrization for all continuous paths. This parametrization is based on an alternative notion of path length, which we call len. Like Euclidean path length, len is invariant under isometries of Rn, is monotone with respect to sub-paths, and for any two points in Rn the straight line segment between them has minimal len length. Unlike Euclidean path length, the len length of any path is defined (i.e., finite) and len is continuous relative to the uniform distance between paths. We use this notion to obtain characterizations of those families of paths which can be reparameterized to be equicontinuous or compact. Finally, we use this parametrization to obtain a canonical homeomorphism between certain families of arcs.