Related papers: How to force a countably tight, initially {\omega}…

We establish a free analogue of Obata's rigidity theorem. More precisely, Cheng and Zhou (2017) proved that on a weighted Riemannian manifold, the sharp spectral gap (Poincar\'e constant) is achieved only when the space splits isometrically…

The space ${\mathcal A}$ of almost complex structures on a closed manifold $M$ is studied. A natural parametrization of the space ${\mathcal A}$ is defined. It is shown, that ${\mathcal A}$ is a infinite dimensional complex weak…

We construct a metric space whose transfinite asymptotic dimension and complementary-finite asymptotic dimension are both omega+1, where omega is the smallest infinite ordinal number. Therefore, we prove that the omega conjecture is not…

We propose a sequential topology on the space of sub-$\sigma$-algebras of a separable probability space $(\Omega,\mathcal{F},\mathbb{P})$ by linking conditional expectations on $L^{2}$ along sequences of sub-$\sigma$-algebras. The varying…

We study the relations between a generalization of pseudocompactness, named $(\kappa, M)$-pseudocompactness, the countably compactness of subspaces of $\beta \omega$ and the pseudocompactness of their hyperspaces. We show, by assuming the…

We introduce a forcing that adds a $\square(\aleph_2,\aleph_0)$-sequence with countable conditions under CH. Assuming the consistency of a weakly compact cardinal, we can find a forcing extension by our new poset in which both…

This paper considers two notions of effective dimension for quadrature in weighted pre-Sobolev spaces with dominating mixed partial derivatives. We begin by finding a ball in those spaces just barely large enough to contain a function with…

Given a Tychonoff space $X$, let $F(X)$ and $A(X)$ be respectively the free topological group and the free Abelian topological group over $X$ in the sense of Markov. In this paper, we consider two topological properties of $F(X)$ or $A(X)$,…

We work in set-theory without choice $\ZF$. Given a closed subset $F$ of $[0,1]^I$ which is a bounded subset of $\ell^1(I)$ ({\em resp.} such that $F \subseteq \ell^0(I)$), we show that the countable axiom of choice for finite subsets of…

We obtain some rigidity results for metrics whose Schouten tensor is bounded from below after conformal transformations. Liang Cheng recently proved that a complete, nonflat, locally conformally flat manifold with Ricci pinching condition…

Let $L^0$ be the vector space of all (equivalence classes of) real-valued random variables built over a probability space $(\Omega, \mathcal{F}, P)$, equipped with a metric topology compatible with convergence in probability. In this work,…

In this work we prove that if $X$ is a complete locally convex space and $f:X\to \mathbb{R}\cup \{+\infty \}$ is a function such that $f-x^\ast$ attains its minimum for every $x^\ast \in U$, where $U$ is an open set with respect to the…

In this note, as a particular case of a more general result, we obtain the following theorem: Let $\Omega\subseteq {\bf R}^n$ be a non-empty bounded open set and let $f:\overline {\Omega}\to {\bf R}^n$ be a continuous function which is…

Motivated by Schoen's conjecture on the volume functional for closed hyperbolic manifolds, we generalize the volume comparison theorem of Hu, Ji, and Shi and establish a volume comparison theorem for rank 1 symmetric spaces of non-compact…

Compact, flat Friedmann-Lemaitre-Robertson-Walker (FLRW) models have recently regained interest as a good fit to the observed cosmic microwave background temperature fluctuations. However, it is generally thought that a globally,…

We here investigate a modification of the compressible barotropic Euler system with friction, involving a fuzzy nonlocal pressure term in place of the conventional one. This nonlocal term is parameterized by $\epsilon$ > 0 and formally…

The two main results of this work are the following: if a space $X$ is such that player II has a winning strategy in the game $\gone(\Omega_x, \Omega_x)$ for every $x \in X$, then $X$ is productively countably tight. On the other hand, if a…

We characterize the finite dimensional asymmetric normed spaces which are right bounded and the relation of this property with the natural compactness properties of the unit ball, as compactness and strong compactness. In contrast with some…

In this paper we discuss the structure of weighted weak Lebesgue spaces and weighted weak Orlicz spaces on $\mathbb{R}^n$. First, we present sufficient and necessary conditions for inclusion relation between weighted weak Lebesgue spaces.…

Let $(A_0, A_1)$ be an interpolation couple, and let $B_j$ be the closure of $A_0^\ast \cap A_1^\ast$ in $A_j^\ast$, $j = 0, 1$. For every $\theta \in \, ]0, 1[$, there exists a natural one to one contraction $R^\theta : A^\theta…