关于渐近维数的超限扩张

A metric space with transfinite asymptotic dimension $2ω$

We build an example of a metric space with transfinite asymptotic dimension $2ω$.

A metric space with transfinite asymptotic dimension $2ω+1$

We construct a metric space whose transfinite asymptotic dimension and complementary-finite asymptotic dimension $2ω+1$.

On metric spaces with given transfinite asymptotic dimensions

For every countable ordinal number $ξ$, we construct a metric space $X_ξ$ whose transfinite asymptotic dimension and complementary-finite asymptotic dimension are both $ξ$.

超限渐近维数

Transfinite Asymptotic Dimension

Dranishnikos在度量空间中引入了渐近性质C，作为有限渐近维数asdim的推广.证明了这一性质可以看作是渐近维数的超限扩展。最初的定义是由Radul给出的。引入了三个等价定义，证明了渐近性质C在乘积下是闭的（公开问题“拓扑学中的公开问题II”），并证明了其它一些事实，即通过定义度量空间族的维数.给出了具有可数超有限渐近维数空间的一些例子。我们还制定了开放的问题和状态“欧米茄猜想”，这启发了本文的大部分。

Examples of metric spaces with asymptotic property $C$

We construct a class of metric spaces whose transfinite asymptotic dimension and complementary-finite asymptotic dimension are both $ω+k$ for any $k\in\mathbb{N}$, where $ω$ is the smallest infinite ordinal number and a metric space whose transfinite asymptotic dimension and complementary-finite asymptotic dimension are both $2ω$. Moreover, we study the relationship between asymptotic dimension growth, transfinite asymptotic dimension and finite decomposition complexity.

渐近大归纳维数的加法与子空间定理

Addition and subspace theorems for asymptotic large inductive dimension

证明了渐近大归纳维数的加法定理和子空间定理。我们调查了这个维度的超限扩展，并表明它是平凡的。