Related papers: Characterizing Corson and Valdivia compact spaces

Let $\mathcal{F} $ be a pointwise almost periodic decomposition of a compact metrizable space $X$. Then $\mathcal{F} $ is $R$-closed if and only if $\hat{\mathcal{F}} $ is usc. Moreover, if there is a finite index normal subgroup $H$ of an…

We describe the singular locus of the compactification of the moduli space $R_{g,l}$ of curves of genus $g$ paired with an $l$-torsion point in their Jacobian. Generalising previous work for $l\le 2$, we also describe the sublocus of…

For a subspace arrangement over a finite field we study the evaluation code defined on the arrangement's set of points. The length of this code is given by the subspace arrangement's characteristic polynomial. For coordinate subspace…

We introduce and study a new class of compactified Jacobians for nodal curves, that we call compactified Jacobians of vine type, or simply V-compactified Jacobians. This class is strictly larger than the class of classical compactified…

We give two characterizations of cones over ellipsoids. Let $C$ be a closed pointed convex linear cone in a finite-dimensional real vector space. We show that $C$ is a cone over an ellipsoid if and only if the affine span of $\partial C…

We give a complete characterization of invariant subspaces for $(M_{z_1}, \ldots, M_{z_n})$ on the Hardy space $H^2(\mathbb{D}^n)$ over the unit polydisc $\mathbb{D}^n$ in $\mathbb{C}^n$, $n >1$. In particular, this yields a complete set of…

We analyze the embedding properties between Besov spaces, defined on the total space $\mathbb R^n$ and on bounded domains. We give a complete classification on whether or not these embedding maps satisfy certain weak compactness…

The aim of this paper is to introduce the concept of Delta-Compact spaces along with some basic properties of it. Here, we try to establish the behavior of Delta-Compact spaces under the continuous mapping. Finally, we define another…

A shape of a combinatorial polytope is a convex embedding into Euclidean space. We provide necessary and sufficient conditions for a piecewise linear map between two shapes of the same polytope to be a compression (respectively a weak…

We discuss role of partially gravitating scalar fields, scalar fields whose energy-momentum tensors vanish for a subset of dimensions, in dynamical compactification of a given set of dimensions. We show that the resulting spacetime exhibits…

We introduce natural strengthenings of sequential compactness called the $r$-Ramsey property for each natural number $r\geq 1$. We prove that metrizable compact spaces are $r$-Ramsey for all $r$ and give examples of compact spaces that are…

The difference of the resolvents of two Laplacians on a half-space subject to Robin boundary conditions is studied. In general this difference is not compact, but it will be shown that it is compact and even belongs to some…

In this paper we describe compactified universal Jacobians, i.e. compactifications of the moduli space of line bundles on smooth curves obtained as moduli spaces of rank 1 torsion-free sheaves on stable curves, using an approach due to…

Under a mild technical assumption, we prove a necessary and sufficient condition for a totally real compacdt set in $\mathbb{C}^n$ to be rationally convex. This generalizes a classical result of Duval-Sibony

We give a new and elementary proof showing that a homeomorphism of a compact metric space is positively expansive if and only if the space is finite.

Consider the moduli space M^0 of arrangements of n hyperplanes in general position in projective (r-1)-space. When r=2 the space has a compactification given by the moduli space of stable curves of genus 0 with n marked points. In higher…

We prove that an isometric action of a compact Lie group on a compact symmetric space is variationally complete if and only if it is hyperpolar.

We give a combinatorial characterization of countable submaximal subspaces of $2^\kappa$. Using a parametrized version of Mathias forcing, we prove that there exists a countable submaximal subspace of $2^{\omega_1}$ whilst…

A compact Riemannian homogeneous space $G/H$, with a bi--invariant orthogonal decomposition $\mathfrak{g}=\mathfrak{h}+\mathfrak{m}$ is called positively curved for commuting pairs, if the sectional curvature vanishes for any tangent plane…

Monotone determined spaces are natural topological extensions of dcpo. Its main purpose is to build an extended framework for domain theory. In this paper, we study the one-step closure and ideal convergence on monotone determined space.…