Related papers: On compact trees with the coarse wedge topology

In this paper, in particular, we prove the following result: Let $E$ be a reflexive real Banach space and let $C\subset E$ be a closed convex set, with non-empty interior, whose boundary is sequentially weakly closed and non-convex. Then,…

The monadic second-order theory of trees allows quantification over elements and over arbitrary subsets. We classify the class of trees with respect to the question: does a tree T have definable Skolem functions (by a monadic formula with…

In this paper, we obtain a minimax theorem by means of which, in turn, we prove the following result: Let $E$ be an infinite-dimensional reflexive real Banach space, $T:E\to E$ a non-zero compact linear operator, $\varphi:E\to {\bf R}$ a…

Bennett, Iosevich and Taylor proved that compact subsets of ${\Bbb R}^d$, $d \ge 2$, of Hausdorff dimensions greater than $\frac{d+1}{2}$ contain chains of arbitrary length with gaps in a non-trivial interval. In this paper we generalize…

We study compactness and L\"owenheim-Skolem properties of fragments of the class-sized logic $\mathcal{L}_{\infty \infty}$ and of class-sized versions of second-order and sort logics. In these fragments, certain combinations of infinitary…

In the recent paper \cite{Aza:19} D Azagra studies the global shape of continuous convex functions defined on a Banach space $X$. More precisely, when $X$ is separable, it is shown that for every continuous convex function…

The cactus of a pointed graph is a discrete tree associated with this graph. Similarly, with every pointed geodesic metric space $E$, one can associate an $\R$-tree called the continuous cactus of $E$. We prove under general assumptions…

We consider special subclasses of the class of Lindel\"of Sigma-spaces obtained by imposing restrictions on the weight of the elements of compact covers that admit countable networks: A space $X$ is in the class $L\Sigma(\leq\kappa)$ if it…

We consider operators T : M_0 -> Z and T : M -> Z, where Z is a Banach space and (M_0, M) is a pair of Banach spaces belonging to a general construction in which M is defined by a "big-O" condition and M_0 is given by the corresponding…

Murota et al. have recently developed a theory of discrete convex analysis which concerns M-convex functions on jump systems. We introduce here a family of M-concave functions arising naturally from polynomials (over a field of generalized…

We investigate the coarse homology of leaves in foliations of compact manifolds. This is motivated by the observation that the non-leaves constructed by Schweitzer and by Zeghib all have non-finitely generated coarse homology. This led us…

Given the tropicalization of a complex subvariety of the torus, we define a morphism between the tropical cohomology and the rational cohomology of their respective tropical compactifications. We say that the subvariety of the torus is…

Let $\mathbf{TB}$ be the category of totally bounded, locally compact metric spaces with the $C_0$ coarse structures. We show that if $X$ and $Y$ are in $\mathbf{TB}$ then $X$ and $Y$ are coarsely equivalent if and only if their Higson…

We obtain exhaustive results and treat in a unified way the question of boundedness, compactness, and weak compactness of composition operators from the Bloch space into any space from a large family of conformally invariant spaces that…

We analyse the structure of the quotient $\mathrm{A}_\sim(\Gamma,X,\mu)$ of the space of measure-preserving actions of a countable discrete group by the relation of weak equivalence. This space carries a natural operation of convex…

We deal with topological spaces homeomorphic to their respective squares. Primarily, we investigate the existence of large families of such spaces in some subclasses of compact metrizable spaces. As our main result we show that there is a…

For a bounded weak Lipschitz domain we show the so called `Maxwell compactness property', that is, the space of square integrable vector fields having square integrable weak rotation and divergence and satisfying mixed tangential and normal…

Let $X$ and $Y$ be separable Banach spaces. Suppose $Y$ either has a shrinking basis or $Y$ is isomorphic to $C(2^\mathbb{N})$ and $A$ is a subset of weakly compact operators from $X$ to $Y$ which is analytic in the strong operator…

We consider some distinguished classes of elements of a multiplicative lattice endowed with coarse lower topologies, and call them lower spaces. The primary objective of this paper is to study the topological properties of these lower…

We study $p$-limited and almost $p$-limited sets in Banach lattices and their connections with relatively $p$-compact and relatively compact sets. We investigate the weak and the strong Gelfand-Phillips property of order $p$, as well as the…