地图的外延维数和完备性

关于扩张维数的几个映射定理

Some mapping theorems for extensional dimension

本文给出了关于有限维空间映射几何的Pakkov和Torunczyk定理的一些结果。

k维映射的逼近

Approximation of k-dimensional maps

本文证明了B.A. Paglikov和V.V. Uspenskij。我们也得到了一些部分的结果，肯定地回答了这些问题。作为这些结果的推论，我们得到了Hurewicz公式在外延维数上的推广。

参数化Bing和Krasinkiewicz地图：再访

Parametric Bing and Krasinkiewicz maps: revisited

令$M$是完备度量$ANR$ -空间，使得对于任何度量紧$K$，函数空间$C(K,M)$包含Bing的稠密集（分别为，Krasinkiewicz）地图。本文证明了$M$具有如下性质：如果$f\colon X\to Y$是度量空间之间的完美满射，则具有源限制拓扑的$C(X,M)$包含稠密的$G_δ$ -映射子集$g$，使得所有的限制$g|f^{-1}(y)$，$y\in Y$都是必应的（分别为，Krasinkiewicz）地图。我们应用上述结果建立了一些关于扩张维数的映射定理。

A completion construction for continuous dynamical systems

In this work we construct the $\Co^{\r}$-completion and $\Co^ł$-completion of a dynamical system. If $X$ is a flow, we construct canonical maps $X\to \Co^{\r}(X)$ and $X\to \Co^ł(X)$ and when these maps are homeomorphism we have the class of $\Co^{\r}$-complete and $\Co^ł$-complete flows, respectively. In this study we find out many relations between the topological properties of the completions and the dynamical properties of a given flow. In the case of a complete flow this gives interesting relations between the topological properties (separability properties, compactness, convergence of ne…

扩张维数与拟有限CW-复形

Extension dimension and quasi-finite CW-complexes

我们通过考虑不一定可数的复形来扩展准有限复形的定义。我们利用L-可逆映射和紧化的维数性质给出了拟有限复形的一个刻画。建立了与拟有限复形类相关的几个结果，如可度量化空间的完备化、泛空间的存在性和因子分解定理的一个版本。进一步，我们推广了UV（L）-空间在非紧情形下的定义，并证明了UV（n）-空间和UV（n）-映射的一些性质分别对UV（L）-空间和UV（L）-映射仍然成立。

The completion of the hyperspace of finite subsets, endowed with the $\ell^1$-metric

For a metric space $X$, let $\mathsf FX$ be the space of all nonempty finite subsets of $X$ endowed with the largest metric $d^1_{\mathsf FX}$ such that for every $n\in\mathbb N$ the map $X^n\to\mathsf FX$, $(x_1,\dots,x_n)\mapsto \{x_1,\dots,x_n\}$, is non-expanding with respect to the $\ell^1$-metric on $X^n$. We study the completion of the metric space $\mathsf F^1\!X=(\mathsf FX,d^1_{\mathsf FX})$ and prove that it coincides with the space $\mathsf Z^1\!X$ of nonempty compact subsets of $X$ that have zero length (defined with the help of graphs). We prove that each subset of zero length in…