Related papers: Selectors of discrete coarse spaces

This paper aims to study the dual of an extended locally convex space. In particular, we study the weak and weak* topologies as well as the topology of uniform convergence on bounded subsets of an extended locally convex space. As an…

We consider a class of bounded linear operators between Banach spaces, which we call operators with the Kato property, that includes the family of strictly singular operators between those spaces. We show that if $T:E\to F$ is a dense-range…

Let $f : X \to S$ be a family of smooth projective algebraic varieties over a smooth connected quasi-projective base $S$, and let $\mathbb{V} = R^{2k} f_{*} \mathbb{Z}(k)$ be the integral variation of Hodge structure coming from degree $2k$…

We use a counting argument and surgery theory to show that if $D$ is a sufficiently general algebraic hypersurface in $\Bbb C^n$, then any local diffeomorphism $F:X \to \Bbb C^n$ of simply connected manifolds which is a $d$-sheeted cover…

Let ${\bf x}=(x_n)_n$ be a sequence in a Banach space. A set $A\subseteq \mathbb{N}$ is perfectly bounded, if there is $M$ such that $\|\sum_{n\in F}x_n\|\leq M$ for every finite $F\subseteq A$. The collection $B({\bf x})$ of all perfectly…

Using an obstruction based on Donaldson's theorem, we derive strong restrictions on when a Seifert fibered space $Y = F(e; \frac{p_1}{q_1}, \ldots, \frac{p_k}{q_k})$ over an orientable base surface $F$ can smoothly embed in $S^4$. This…

Lineability is a property enjoyed by some subsets within a vector space X. A subset A of X is called lineable whenever A contains, except for zero, an infinite dimensional vector subspace. If, additionally, X is endowed with richer…

Ordered vector spaces E and F are said to be order isomorphic if there is a (not necessarily linear) bijection between them that preserves order. We investigate some situations under which an order isomorphism between two Banach lattices…

When a linear order has an order preserving surjection onto each of its suborders we say that it is strongly surjective. We prove that the set of countable strongly surjective linear orders is complete for the class of sets which are the…

Every left-invariant ordering of a group is either discrete, meaning there is a least element greater than the identity, or dense. Corresponding to this dichotomy, the spaces of left, Conradian, and bi-orderings of a group are naturally…

In the first part of our note we prove that every Weakly Lindel\"of Determined (WLD) (in particular, every reflexive) non-separable Banach $X$ space contains two dense linear subspaces $Y$ and $Z$ that are not densely isomorphic. This means…

We study some closure-type properties of function spaces endowed with the new topology of strong uniform convergence on a bornology introduced by Beer and Levy in 2009. The study of these function spaces was initiated in [2] and [3]. The…

We construct a family $(\mathcal{X}_\al)_{\al\le \omega_1}$ of reflexive Banach spaces with long transfinite bases but with no unconditional basic sequences. In our spaces $\mathcal{X}_\al$ every bounded operator $T$ is split into its…

A complex variety $X$ admits a cellular resolution of singularities if there exists a resolution of singularities $\widetilde X\to X$ such that its exceptional locus as well as $\widetilde X$ and the singular locus of $X$ admit a cellular…

A set $E$ in a Banach space $X$ is compactivorous if for every compact set $K$ in $X$ there is a nonempty, (relatively) open subset of $K$ which can be translated into $E$. In a separable Banach space, this is a sufficient condition which…

We prove that every usco multimap $\Phi:X\to Y$ from a metrizable separable space $X$ to a GO-space $Y$ has an $F_\sigma$-measurable selection. On the other hand, for the split interval $\ddot{\mathbb I}$ and the projection $P:\ddot{\mathbb…

Let ${\cal E}$ be a topos, ${{\rm Dec}({\cal E}) \rightarrow {\cal E}}$ be the full subcategory of decidable objects, and ${{\cal E}_{\neg\neg} \rightarrow {\cal E}}$ be the full subcategory of double-negation sheaves. We give sufficient…

We continue the development of the study of the equisingularity of isolated singularities, in the determinantal case. This version of the paper includes a substantial amount of new material (76% larger). The new material introduces the idea…

A topological space is called Loeb if the collection of all its non-empty closed sets has a choice function. In this article, in the absence of the axiom of choice, connections between Loeb and sequential spaces are investigated. Among…

Diffeological spaces are generalizations of smooth manifolds. In this paper, we study the homotopy theory of diffeological spaces. We begin by proving basic properties of the smooth homotopy groups that we will need later. Then we introduce…