A metric space with transfinite asymptotic dimension $2ω$

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.

Transfinite Sequences of Continuous and Baire Class 1 Functions

The set of continuous or Baire class 1 functions defined on a metric space $X$ is endowed with the natural pointwise partial order. We investigate how the possible lengths of well-ordered monotone sequences (with respect to this order) depend on the space $X$.

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。

Countable ordinal spaces and compact countable subsets of a metric space

We show in detail that every compact countable subset of a metric space is homeomorphic to a countable ordinal number, which extends a result given by Mazurkiewicz and Sierpinski for finite-dimensional Euclidean spaces. In order to achieve this goal, we use Transfinite Induction to construct a specific homeomorphism. In addition, we prove that for all metric space $(E,d)$, the cardinality of the set of all the equivalence classes $\mathscr{K}_E$, up to homeomorphisms, of compact countable subsets of $E$ is less than or equal to $\aleph_1$, i.e. $|\mathscr{K}_E| \le \aleph_1$. We also show that…

模糊度量空间的渐近维数

Asymptotic dimension of fuzzy metric spaces

该研究定义了George和Veeramini意义下模糊度量空间的渐近维数，证明其为粗范畴不变量，推导相关推论并计算了部分模糊度量空间的渐近维数。

There is no universal proper metric spaces for asymptotic dimension 1

Answering a question of Ma, Siegert, and Dydak we show that there is no universal proper metric space for the asymptotic dimension $n\ge1$.

Asymptotically Scattered Spaces

We define thin and asymptotically scattered metric spaces as asymptotic counterparts of discrete and scattered metric spaces respectively. We characterize asymptotically scattered spaces in terms of prohibited subspaces, and classify thin metric spaces up to coarse equivalence. We introduce the types of asymptotically scattered spaces and construct the spaces of distinct types. We transfer the notion of asymptotically scattered spaces to $G$-spaces and characterize asymptotically scattered spaces of groups.