Related papers: Quotients, $\ell_\infty$ and abstract Ces\`aro spa…

We study the random binary contingency tables with non-uniform margin. More precisely, for parameters $n,\delta,B,C$, we consider $X=(X_{ij})$ with $X_{ij}\in \lbrace 0,1\rbrace$, the random binary contingency tables whose first…

We find necessary and sufficient conditions under which an arbitrary metric space $X$ has a unique pretangent space at the marked point $a\in X$. Key words: Metric spaces; Tangent spaces to metric spaces; Uniqueness of tangent metric…

Unbounded composition operators in $L^2$-space over discrete measure spaces are investigated. Normal, formally normal and quasinormal composition operators acting in $L^2$-spaces of this kind are characterized.

We study lattices in non-positively curved metric spaces. Borel density is established in that setting as well as a form of Mostow rigidity. A converse to the flat torus theorem is provided. Geometric arithmeticity results are obtained…

We expand \v{C}ech cohomology of a topological space $X$ with values in a presheaf on $X$ to \v{C}ech cohomology of a commutative ring with unity $R$ with values in a presheaf on $R$. The strategy is to observe that both the set of open…

A $k_\omega$-space $X$ is a Hausdorff quotient of a locally compact, $\sigma$-compact Hausdorff space. A theorem of Morita's describes the structure of $X$ when the quotient map is closed, but in 2010 a question of Arkhangel'skii's…

Let $X$ be a sequence space and denote by $Z(X)$ the subset of $X$ formed by sequences having only a finite number of zero coordinates. We study algebraic properties of $Z(X)$ and show (among other results) that (for $p \in [1,\infty]$)…

In the sequel, we recall and comment some classical results on the non-increasing rearrangement and Lorentz spaces. There are papers in the existing literature that seemed to have been bypassed as regards its contractive property in~$L^p$…

In this paper it were investigated the algebraic and topological properties of the space \mathscr{C}_f, which consists of convergent sequences of uncertain variable intervals. It was established that \mathscr{C}_f is a normed space with a…

Let $L(X)$ be the free locally convex space over a Tychonoff space $X$. We show that the following assertions are equivalent: (i) $L(X)$ is $\ell_\infty$-barrelled, (ii) $L(X)$ is $\ell_\infty$-quasibarrelled, (iii) $L(X)$ is…

We show that for any metric space $X$ the condition \[ \int_X\int_X\int_X c(z_1,z_2,z_3)^2\, d\Hm z_1\, d\Hm z_2\, d\Hm z_3 < \infty, \] where $c(z_1,z_2,z_3)$ is the Menger curvature of the triple $(z_1,z_2,z_3)$, guarantees that $X$ is…

We show that the norm of the commutator defines "almost a metric" on the quotient space of commuting matrices, in the sense that it is a semi-metric satisfying the triangle inequality asymptotically for large matrices drawn from a "good"…

Let $X$ be a continuum and let $C(X)$ denote the hyperspace of subcontinua of $X$, endowed with the Hausdorff metric. For $p\in X$, define the hyperspace $C(p,X)=\{A\in C(X):p\in A\}$ as a subspace of $C(X)$. In this paper we introduced the…

A metric measure space $(X,d,\mu)$ is said to be $A_{\infty}$ on curves if there exist constants $\tau < 1$ and $\theta > 0$ with the following property. For every $x \in X$, $0 < r \leq \mathrm{diam}(X)$, and a Borel set $S \subset B(x,r)$…

Grafakos systematically proved that $A_\infty$ weights have different characterizations for cubes in Euclidean spaces in his classical text book. Very recently, Duoandikoetxea, Mart\'{\i}n-Reyes, Ombrosi and Kosz discussed several…

Following results of Bourgain and Gorelik we show that the spaces $\ell_p$, $1<p<\infty$, as well as some related spaces have the following uniqueness property: If $X$ is a Banach space uniformly homeomorphic to one of these spaces then it…

The existence of an equidimensional morphism f with etale local sections from a regular algebraic space X to a locally noetherian normal algebraic space S of characteristic zero with excellent local rings implies that S is regular and f…

In this paper we construct a closed subspace $X\subset C[0,1]$ with countable oscillating spectrum $\Omega(X)$ such that $X$ is isometric to $\ell^1$. This provides a negative answer to Question~4.3 posed by Enflo, Gurariy, and Seoane in…

Suppose that a real nonatomic function space on $[0,1]$ is equipped with two re\-arran\-ge\-ment-invariant norms $\|\cdot\|$ and $|||\cdot|||$. We study the question whether or not the fact that $(X,\|\cdot\|)$ is isometric to…

We give a new proof of the completeness of the space $\mathcal{O}_C$ by applying a criterion of compact regularity for the isomorphic sequence space $\lim_{k\rightarrow} (s\hat \otimes (\ell^\infty)_{-k})$. Along the way we show that the…