度量空间中的Lipschitz道路及其*积运算

摘要

In this paper, Lipschitz paths in a metric space are introduced and discussed. Some properties of Lipschitz paths are obtained, it is proved that the union of two Lipschitz paths that are not disjoint is also a Lipschitz path. The *-products of two Lipschitz paths are defined, it is proved that if E,F are Lipschitz paths in metric spaces X,Y, respectively and h: [0,1]→E as well as g:[0,l]→F are Lipschitz surjections, then * -product E * F∣(h,g) of E and F with respect to (h, g) is also a Lipschitz path in the product space X×Y.%通过距离空间(X,d)上Lipschitz映射,引入了X中的Lipschitz道路的概念,研究了它的一些性质,证明了同一度量空间中两个相交的Lipschitz道路的并也是Lipschitz道路.引入了度量空间X,Y中的Lipschitz道路E,F关于h:[0,1]→E与g:[0,1]→F的*-积E*F｜(h.g),证明了当h,g都是Lipschitz满射时E*F｜(h,g)为乘积空间X×Y中的Lipschitz道路.