Related papers: Perfect maps between submetrizable spaces

A topological space is nonseparably connected if it is connected but all of its connected separable subspaces are singletons. We show that each connected sequential topological space X is the image of a nonseparably connected complete…

If $X$ is a (topological) space, the $n$th finite subset space of $X$, denoted by $X(n)$, consists of $n$-point subsets of $X$ (i.e., nonempty subsets of cardinality at most $n$) with the quotient topology induced by the unordering map…

We prove the equivalence between geometric and analytic definitions of quasiconformality for a homeomorphism $f\colon X\rightarrow Y$ between arbitrary locally finite separable metric measure spaces, assuming no metric hypotheses on either…

For any countable $CW$-complex $K$ and a cardinal number $\tau\geq\omega$ we construct a completely metrizable space $X(K,\tau)$ of weight $\tau$ with the following properties: $\e X(K,\tau)\leq K$, $X(K,\tau)$ is an absolute extensor for…

Let $R=\mathbb{F}_p$ or a field of characteristic $0$. For each $R$-good topological space $Y$, we define a collection of higher cohomology operations which, together with the cohomology algebra $H^*(Y;R)$ suffice to determine $Y$ up to…

The deck of a topological space $X$ is the set $\mathcal{D}(X)=\{[X \setminus \{x\}] \colon x \in X\}$, where $[Z]$ denotes the homeomorphism class of $Z$. A space $X$ is topologically reconstructible if whenever…

An ultrametric preserving function $f$ is said to be strongly ultrametric preserving if ultrametrics $d$ and $f \circ d$ define the same topology on $X$ for each ultrametric space $(X,d)$. The set of all strongly ultrametric preserving…

We construct a multiset space $\mathbb{N}[X]$ over a metric space $X$ that simultaneously enjoys desirable topological properties and admits a natural matching metric $d_{\mathbb{N}[X]}$, making it a metrizable abelian topological monoid…

Let $(X,d)$ be a finite ultrametric space. In 1961 E.C. Gomory and T.C. Hu proved the inequality $|Sp(X)|\leqslant |X|$ where $Sp(X)=\{d(x,y)\colon x,y \in X\}$. Using weighted Hamiltonian cycles and weighted Hamiltonian paths we give new…

We show that a topometric space $X$ is topometrically isomorphic to a type space of some continuous first-order theory if and only if $X$ is compact and has an open metric (i.e., satisfies that $\{p : d(p,U) < \varepsilon\}$ is open for…

The present paper generalizes the result from one of the papers by Galstyan. Namely, we consider two nonempty subsets $A$ and $B$ of a metric space $X$, and construct one-parametric family $F_r$ of subsets obtained by intersection between…

We introduce a class of mappings called vertical quasi-isometries and show that branched quasisymmetries $X\to Y$ of Guo and Williams between compact, bounded turning metric doubling spaces admit natural vertically quasi-isometric…

Finite metric spaces arise in many different contexts. Enormous bodies of data, scientific, commercial and others can often be viewed as large metric spaces. It turns out that the metric of graphs reveals a lot of interesting information.…

Given a flat metric one may generate a local Hamiltonian structure via the fundamental result of Dubrovin and Novikov. More generally, a flat pencil of metrics will generate a local bi-Hamiltonian structure, and with additional…

For a map f: X -> Y of quasi-compact quasi-separated schemes, we discuss quasi-perfection, that is, the right adjoint f^\times of the derived functor Rf_* respects small direct sums. This is equivalent to the existence of a functorial…

Let $(X, d)$ be a compact metric space and let $\mathcal{M}(X)$ denote the space of all finite signed Borel measures on $X$. Define $I \colon \mathcal{M}(X) \to \R$ by \[ I(\mu) = \int_X \int_X d(x,y) d\mu(x) d\mu(y), \] and set $M(X) =…

Let $(X, \mathscr{L}, \lambda)$ and $(Y, \mathscr{M}, \mu)$ be finite measure spaces for which there exist $A \in \mathscr{L}$ and $B \in \mathscr{M}$ with either $0 < \lambda(A) < 1 < \lambda(X)$ and $0 < \mu(B) < \mu(Y)$, or the other way…

For separable metrizable spaces $X,Y$ and a metrizable topological group $Z$ by $S(X\times Y,Z)$ we denote the space of all separately continuous functions $f:X\times Y\to Z$ endowed with the topology of layer-wise uniform convergence,…

It is shown that a locally finite ultrametric space $(X, d)$ is generated by labeled tree if and only if, for every open ball $B \subseteq X$, there is a point $c \in B$ such that $d(x, c) = \operatorname{diam} B$ whenever $x \in B$ and $x…

Let (X,d) be a metric space and m\in X. Suppose that \phi:X\times X\to\mathbold{R} is a nonnegative symmetric function. We define a metric d^{\phi,m} on X which is equivalent to d. If d^{\phi,m} is totally bounded, its completion is a…