Related papers: Semi-Eberlein spaces

The aim of this paper is to study the topological properties of some classes of subsemimodules endowed with a subbasis closed-set topology. We show that such spaces are $T_0$. When the semimodule is finitely generated, those spaces are…

Answering some of the main questions from [MR13], we show that whenever $\kappa$ is a cardinal satisfying $\kappa^{< \kappa} = \kappa > \omega$, then the embeddability relation between $\kappa$-sized structures is strongly invariantly…

The "weakly Hausdorff" property for pseudoradial spaces fails to be naturally characterized by unique convergence of transfinite sequences. In response, we develop the category $\mathbf{SPsRad}$ of strongly pseudoradial spaces, compactly…

We prove a compact embedding theorem in a class of spaces of piecewise H1 functions subordinated to a class of shape regular, but not necessarily quasi-uniform triangulations of a polygonal domain. This result generalizes the…

We extend Korevaar-Schoen's theory of metric valued Sobolev maps to cover the case of the source space being an RCD space. In this situation it appears that no version of the `subpartition lemma' holds: to obtain both existence of the limit…

In this paper, a new class of Sobolev spaces with kernel function satisfying a L\'evy-integrability type condition on compact Riemannian manifolds is presented. We establish the properties of separability, reflexivity, and completeness. An…

In this paper, we prove that if $\kappa$ is a almost strongly compact cardinal, then any MAEC with L\"owenheim-Skolem number below $\kappa$ is $<\kappa$-d-tame.

All spaces are assumed to be Tychonoff. Given a realcompact space $X$, we denote by $\mathsf{Exp}(X)$ the smallest infinite cardinal $\kappa$ such that $X$ is homeomorphic to a closed subspace of $\mathbb{R}^\kappa$. Our main result shows…

We obtain an internal topological characterization of the subspaces of Eberlein compacts (respectively, Corson compacts, strong Eberlein compacts, uniform Eberlein compacts, $n$-uniform Eberlein compacts).

Madden has shown that in contrast to the situation with frames, the smallest dense quotient of a $\kappa$-frame need not be Boolean. We characterise these so-called d-reduced $\kappa$-frames as those which may be embedded as a generating…

Brezis and Mironescu have announced several years ago that for a compact manifold $N^n \subset \mathbb{R}^\nu$ and for real numbers $0 < s < 1$ and $1 \le p < \infty$ the class $C^\infty(\overline{Q}^m; N^n)$ of smooth maps on the cube with…

Assuming that there is a stationary set in $\omega_{2}$ of ordinals of countable cofinality that does not reflect, we prove that there exists a compact space which is not Corson compact and whose all continuous images of weight at most…

This paper deals with a class of Sobolev spaces of vector-valued functions on a compact group. Some Sobolev embedding theorems are proved.

We introduce a new class of $\varkappa$-metrizable spaces, namely countably $\varkappa$-metrizable spaces. We show that the class of all $\varkappa$-metrizable spaces is a proper subclass of counably $\varkappa$-metrizable spaces. On the…

By making use of the classification of real simple Lie algebra, we get the maximum of the squared length of restricted roots case by case, thus we get the upper bounds of sectional curvature for irreducible Riemannian symmetric spaces of…

In this paper we prove that $M^p_\Lambda$ is almost isometric to $\ell^p$ in the canonical way when $\Lambda$ is lacunary with a large ratio. On the other hand, our approach can be used to study also the Carleson measures for M\"untz spaces…

It is common that a Sobolev space defined on $\mathbb{R}^m$ has a non-compact embedding into an $L^p$-space, but it has subspaces for which this embedding becomes compact. There are three well known cases of such subspaces, the Rellich…

This paper is devoted to the study of a generalization of Sobolev spaces for small $L^{p}$ exponents, i.e. $0<p<1$. We consider spaces defined as abstract completions of certain classes of smooth functions with respect to weighted…

We discuss two problems concerning the class Eberlein compacta, i.e., weakly compact subspaces of Banach spaces. The first one deals with preservation of some classes of scattered Eberlein compacta under continuous images. The second one…

We establish the asymptotic regularity and the $\Delta$-convergence of the sequence constructed by the alternating projections to closed convex sets in a CAT($\kappa$) space with $\kappa > 0$. Furthermore, the strong convergence of the…