Related papers: The Dyck and the Preiss separation uniformly

For a large class of separable Banach spaces, we prove the real analytic Dolbeault Isomorphism Theorem for open subsets.

We prove that universal differentiability sets in Euclidean spaces possess distinctive structural properties. Namely, we show that any universal differentiability set contains a `kernel' in which the points of differentiability of each…

In a previous work, by extending the classical Quillen construction to the non-simply connected case, we have built a pair of adjoint functors, 'model' and 'realization', between the categories of simplicial sets and complete differential…

Recently geometric hypergraphs that can be defined by intersections of pseudohalfplanes with a finite point set were defined in a purely combinatorial way. This led to extensions of earlier results about points and halfplanes to…

We provide a new foundation for combinatorial commutative algebra and Stanley-Reisner theory using the partition complex introduced in [Adi18]. One of the main advantages is that it is entirely self-contained, using only a minimal knowledge…

We prove a tangle-tree theorem and a tangle duality theorem for abstract separation systems $\vec S$ that are submodular in the structural sense that, for every pair of oriented separations, $\vec S$ contains either their meet or their join…

In a recent work, Andrews gave analytic proofs of two conjectures concerning some variations of two combinatorial identities between partitions of a positive integer into odd parts and partitions into distinct parts discovered by Beck.…

Among other things, we show that the ideal sheaf of a complex Hilbert submanifold of a pseudoconvex open subset of Hilbert space is acyclic over the ambient pseudoconvex open set. We also prove a vanishing theorem for a fairly general class…

In this paper, we prove some new thickness theorems with partial derivatives. We give some applications. First, we give a simple criterion that can judge whether two scaled Cantor sets have non-empty intersection. Second, we prove under…

We give a simpler proof for the local well-posedness of the modified Korteweg-de Vries equations and modified Benjamin-Ono equation in $H^{\frac{1}{4}}(\mathbb{R})$ and $H^{\frac{1}{2}}(\mathbb{R})$, respectively. The proof is based on the…

We analyze the effective content of countable, second countable topological spaces by directly calculating the complexity of several topologically defined index sets. We focus on the separation principles, calibrating an arithmetic…

We consider a countably generated and uniformly closed algebra of bounded functions. We assume that there is a lower semicontinuous, with respect to the supremum norm, quadratic form and that normal contractions operate in a certain sense.…

We study the class of compact spaces that appear as structure spaces of separable Banach lattices. In other words, we analyze what $C(K)$ spaces appear as principal ideals of separable Banach lattices. Among other things, it is shown that…

In this work, we provide some novel results that establish both the existence of Henig global proper efficient points and their density in the efficient set for vector optimization problems in arbitrary normed spaces. Our results do not…

Our main result marks progress on an old conjecture of Vitushkin. We show that a compact set in the plane with plenty of big projections (PBP) has positive analytic capacity, along with a quantitative lower bound. A higher dimensional…

A closed convex subset of a normed linear space is said to have the strong separation property if it can be strongly separated from every other disjoint closed and convex set by a closed hyperplane. In this paper we give some results on the…

A unique analytic continuation result is proved for solutions of a relatively general class of difference equations, using techniques of generalized Borel summability. This continuation allows for Painlev\'e property methods to be extended…

This paper consists of two prongs. Firstly, we prove that any Specht module labelled by a 2-separated partition is semisimple and we completely determine its decomposition as a direct sum of graded simple modules. Secondly, we apply these…

Let $K$ be a convex body in Euclidean space ${\mathbb R}^d$, and let a translation invariant, locally finite Borel measure on the space of hyperplanes in ${\mathbb R}^d$ be given. For $\delta\ge 0$, we consider the set of all points $x$ for…

We have defined almost separable space. We show that like separability, almost separability is $c$ productive and converse also true under some restrictions. We establish a Baire Category theorem like result in Hausdorff, Pseudocompacts…