Related papers: Existence of continuous euclidean embeddings for a…

We prove that the category of Nachbin's compact ordered spaces and order-preserving continuous maps between them is dually equivalent to a variety of algebras, with operations of at most countable arity. Furthermore, we show that the…

We formalize the observation that the same summability methods converge in a Banach space $X$ and its dual $X^*$. At the same time we determine conditions under which these methods converge in the weak and weak*-topologies on $X$ and $X^*$…

A little known theorem due to Campbell is employed to establish the local embedding of a wide class of 4-dimensional spacetimes in 5-dimensional Ricci-flat spaces. An embedding for the class of n-dimensional Einstein spaces is also found.…

The goal of this paper is to present a complete characterisation of points of order continuity in abstract Ces\`aro function spaces $CX$ for $X$ being a symmetric function space. Under some additional assumptions mentioned result takes the…

The main result is the following. Let $f \colon X \rightarrow Y$ be a continuous mapping of a completely Baire space $X$ onto a hereditary weakly Preiss-Simon regular space $Y$ such that the image of every open subset of $X$ is a resolvable…

It is proven that if $ (X,d) $ is an arbitrary metric space and $ U $ is a path-connected subset of $ X $ with $M:=\{x_i:\ i\in\{1,2,\dots,k\}\}\subset int(U) $, then the property of path-connectedness is also preserved in the resulting set…

We give a sufficient condition for a projective metric on a subset of a Euclidean space to admit a bi-Lipschitz embedding into Euclidean space of the same dimension.

We study rank-one sheaves and stable pairs on a smooth projective complex surface. We obtain an embedding of the moduli space of limit stable pairs into a smooth space. The embedding induces a perfect obstruction theory, which, over a…

This is the sequel to our first paper concerning the balanced embedding of a non-compact complex manifold into an infinite-dimensional projective space. We prove the uniqueness of such an embedding. The proof relies on fine estimates of the…

Let $S$ be a rank-one symmetric space of non-compact type and let $X$ be a $\text{CAT}(-1)$ space. A well-known result by Bourdon states that if a topological embedding $\varphi: \partial_\infty S \rightarrow \partial_\infty X$ respects…

Let $X$ be a union of a sequence of symplectic manifolds of increasing dimension and let $M$ be a manifold with a closed $2$-form $\omega$. We use Tischler's elementary method for constructing symplectic embeddings in complex projective…

A metric space $(X,d)$ has the de Groot property $GP_n$ if for any points $x_0,x_1,...,x_{n+2}\in X$ there are positive indices $i,j,k\le n+2$ such that $i\ne j$ and $d(x_i,x_j)\le d(x_0,x_k)$. If, in addition, $k\in\{i,j\}$ then $X$ is…

We prove that for elliptic and canceling linear differential operators $\mathbb{B}$ of order $n$ on $\mathbb{R}^n$, continuity of a map $u$ can be inferred from the fact that $\mathbb{B} u$ is a measure. We also prove strict continuity of…

We consider a Nevanlinna-Pick interpolation problem on finite sequences of the unit disc D constrained by Hardy and radial-weighted Bergman norms. We find sharp asymptotics on the corresponding interpolation constants. As another…

We study metric measure spaces that admit "thick" families of rectifiable curves or curve fragments, in the form of Alberti representations or curve families of positive modulus. We show that such spaces cannot be bi-Lipschitz embedded into…

Let $R$ be a semilocal principal ideal domain. Two algebraic objects over $R$ in which scalar extension makes sense (e.g. quadratic spaces) are said to be of the same genus if they become isomorphic after extending scalars to all…

We prove two rigidity theorems for open (complete and noncompact) $n$-manifolds $M$ with nonnegative Ricci curvature and the infimum of volume growth order $<2$. The first theorem asserts that the Riemannian universal cover of $M$ has…

Let $\mathcal{I}$ be a meager ideal on $\mathbf{N}$. We show that if $x$ is a sequence with values in a separable metric space then the set of subsequences [resp. permutations] of $x$ which preserve the set of $\mathcal{I}$-cluster points…

A topological space is locally equiconnected if there exists a neighborhood $U$ of the diagonal in $X\times X$ and a continuous map $\lambda:U\times[0,1]\to X$ such that $\lambda(x,y,0)=x$, $\lambda(x,y,1)=y$ et $\lambda(x,x,t)=x$ for…

In this note we obtain the surjectivity of smooth maps into Euclidean spaces under mild conditions. As application we give a new proof of the Fundamental Theorem of Algebra. We also observe that any $C^1$-map from a compact manifold into…