相关论文: Total orders on compact metric spaces and covering…
Adapting a homotopy reconstruction theorem for general metric compacta, we show that every countable metric or ultrametric compact space can be topologically reconstructed as the inverse limit of a sequence of finite $T_0$ spaces which are…
We explore representing the compact subsets of a given represented space by infinite sequences over Plotkin's $\mathbb{T}$. We show that computably compact computable metric spaces admit representations of their compact subsets in such a…
In this paper we provide a criteria for geometric finiteness of Kleinian groups in general dimension. We formulate the concept of conformal finiteness for Kleinian groups in space of dimension higher than two, which generalizes the notion…
In this paper, we will establish a general method of studying finite-dimensional normed spaces, and apply this method to classifying $3$-dimensional and $4$-dimensional normed spaces over a non-spherically complete field. For this purpose,…
We study quasi-modular pseudometric spaces as asymmetric refinements of modular metric structures. To each such space we associate canonical forward and backward quasi-uniformities and the corresponding directional topologies. We introduce…
We first prove that for every metrizable space $X$, for every closed subset $F$ whose complement is zero-dimensional, the space $X$ can be embedded into a product space of the closed subset $F$ and a metrizable zero-dimensional space as a…
For a partially ordered set $(S, \mathord\preceq)$, the order (monotone) dimension is the minimum cardinality of total orders (respectively, real-valued order monotone functions) on $S$ that characterize the order $\preceq$. In this paper…
A topological space is totally paracompact if any base of this space contains a locally finite subcover. We focus on a problem of Curtis whether in the class of regular Lindel\"of spaces total paracompactness is equivalent to the Menger…
We give criteria of total incomparability for certain classes of mixed Tsirelson spaces. We show that spaces of the form $T[(M_k,\theta_k)_{k=1}^{\ell}]$ with index $i(M_k)$ finite are either $c_0$ or $\ell_p$ saturated for some $p$ and we…
The finitistic dimension of a triangulated category is introduced. For the category of perfect complexes over a ring it is shown that this dimension is finite if and only if the small finitistic dimension of the ring is finite.
Results of Sierpinski and others have shown that certain finite-dimensional product sets can be written as unions of subsets, each of which is "narrow" in a corresponding direction; that is, each line in that direction intersects the subset…
We prove a general criterion for a metric space to have conformal dimension one. The conditions are stated in terms of the existence of enough local cut points in the space. We then apply this criterion to the boundaries of hyperbolic…
We show in ZF that: (i) Every subcompact metrizable space is completely metrizable, and every completely metrizable space is countably subcompact. (ii) A metrizable space X=(X,T) is countably compact iff it is countably subcompact relative…
We prove several results of the following type: given finite dimensional normed space V there exists another space X with log (dim X) = O(log (dim V)) and such that every subspace (or quotient) of X, whose dimension is not "too small,"…
It is proved that the square of the Sorgenfrey line has infinite covering dimension.
An infinite structure has the finite length property (over a given field) if, for each of its finite powers, chains of equivariant subspaces in the corresponding free vector space are bounded in length. Prior work showed that the countable…
By recognizing them as fundamental groups of developable complexes of groups we prove that mapping class groups of compact orientable surfaces have finite asymptotic dimension.
We construct a class of metric spaces whose transfinite asymptotic dimension and complementary-finite asymptotic dimension are both $\omega+k$ for any $k\in\mathbb{N}$, where $\omega$ is the smallest infinite ordinal number and a metric…
We prove that the countable product of supercomplete spaces having a countable closed cover consisting of partition-complete subspaces is supercomplete with respect to its metric-fine coreflection. Thus, countable products of…
We define a class of trim metric spaces and show that every finite metric space is the leaf space of a metric forest with trim base.