标题： Lipschitz-自由空间在可数完全离散度量空间上的多样性 显示英文标题

标题： Diversity of Lipschitz-free spaces over countable complete discrete metric spaces

摘要： 我们证明了存在不可数多个彼此非同构的Lipschitz自由空间，它们定义在可数、完备、离散的度量空间上。此外，存在一个可数、完备、离散的度量空间，其自由空间不能嵌入到任何一致离散度量空间的自由空间中。 这种增强的多样性是因为当赋值给超出紧致纯粹1-不可重构空间压抑限制之外的度量空间的自由空间时，可 dentability 指数$D$表现出高度非二元的行为。事实上，可数、完备、离散$\}$的 cardinality$\{D(\mathcal F(M)): M$是不可数的，而无限、紧致、纯粹1-不可重构$\}=\{\omega,\omega^2\}$的$\{D(\mathcal F(M)):M$。 对于一致离散度量空间也观察到了类似的障碍，因为它们的自由空间排除了较高的 dentability 指数值：无限、一致离散$\}=\{\omega^2,\omega^3\}$的$\{D(\mathcal F(M)):M$。 显示英文摘要

摘要： We show that there are uncountably many mutually non-isomorphic Lipschitz-free spaces over countable, complete, discrete metric spaces. Also there is a countable, complete, discrete metric space whose free space does not embed into the free space of any uniformly discrete metric space. This enhanced diversity is a consequence of the fact that the dentability index $D$ presents a highly non-binary behavior when assigned to the free spaces of metric spaces outside of the oppressive confines of compact purely 1-unrectifiable spaces. Indeed, the cardinality of $\{D(\mathcal F(M)): M$ countable, complete, discrete$\}$ is uncountable while $\{D(\mathcal F(M)):M$ infinite, compact, purely 1-unrectifiable$\}=\{\omega,\omega^2\}$. Similar barrier is observed for uniformly discrete metric spaces as higher values of the dentability index are excluded for their free spaces: $\{D(\mathcal F(M)):M$ infinite, uniformly discrete$\}=\{\omega^2,\omega^3\}$.