Related papers: Zero-dimensional $\sigma$-homogeneous spaces

In this note, we verify the classification of local geometries given by A.Z. Petrov. First, we determine criteria for identifying a given 3D Lorentz homogeneous space in Petrov's classification. Then, we identify all inequivalent 1D…

A theorem of Y. Berest, P. Etingof and V. Ginzburg states that finite dimensional irreducible representations of a type A rational Cherednik algebra are classified by one rational number m/n. Every such representation is a representation of…

This paper is devoted to the study of isometrically homogeneous spaces from the view point of metric geometry. Mainly we focus on those spaces that are homeomorphic to lines. One can reduce the study to those distances on $\R$ that are…

In this paper we focus on the set-open topologies on the group $\mathcal{H}(X)$ of all self-homeomorphisms of a topological space $X$ which yield continuity of both the group operations, product and inverse function. As a consequence, we…

We investigate to what extend finite-dimensional homogeneous locally compact $ANR$-spaces have common properties with Euclidean manifolds. Specially, the local structure of homogeneous $ANR$-spaces is described. Using that description, we…

We study homogeneous metric spaces, by which we mean connected, locally compact metric spaces whose isometry group acts transitively. After a review of some classical results, we use the Gleason-Iwasawa-Montgomery-Yamabe-Zippin structure…

We show that, up to Morita equivalence, any finite-dimensional algebra with a suitable homological system, admits an exact Borel subalgebra. This generalizes a theorem by Koenig, K\"ulshammer and Ovsienko, which holds for quasi-hereditary…

Let $S$ be a compact oriented surface. We construct homogeneous quasimorphisms on $Diff(S, area)$, on $Diff_0(S, area)$ and on $Ham(S)$ generalizing the constructions of Gambaudo-Ghys and Polterovich. We prove that there are infinitely many…

We introduce and investigate the notion of (strong) $K^n_G$-manifolds, where $G$ is an abelian group. One of the result related to that notion (Theorem 3.4) implies the following partial answer to the Bing-Borsuk problem \cite{bb}, whether…

We present short proofs of all known topological properties of general Busemann $G$-spaces (at present no other property is known for dimensions more than four). We prove that all small metric spheres in locally $G$-homogeneous Busemann…

We give a proof that every space of weighted square-integrable holomorphic functions admits an equivalent weight whose Bergman kernel has zeroes. Here the weights are equivalent in the sense that they determine the same space of holomorphic…

For a cardinal $\kappa > \omega$ a metric space $X$ is called to be $\kappa$-superuniversal whenever for every metric space $Y$ with $|Y| < \kappa$ every partial isometry from a subset of $Y$ into $X$ can be extended over the whole space…

In this article, the authors establish the pointwise characterization of Besov and Triebel-Lizorkin spaces on spaces of homogeneous type via clarifying the relationship among Haj\l asz-Sobolev spaces, Haj\l asz-Besov and Haj\l…

We study lattices in non-positively curved metric spaces. Borel density is established in that setting as well as a form of Mostow rigidity. A converse to the flat torus theorem is provided. Geometric arithmeticity results are obtained…

We classify noncompact homogeneous spaces which are Einstein and asymptotically harmonic. This completes the classification of Riemannian harmonic spaces in the homogeneous case: Any simply connected homogeneous harmonic space is flat, or…

Below, by space we mean a separable metrizable zero-dimensional space. It is studied when the space can be embedded in a Cantor set while maintaining the algebraic structure. Main results of the work: every space is an open retract of a…

We consider a homogeneous fractional Sobolev space obtained by completion of the space of smooth test functions, with respect to a Sobolev--Slobodecki\u{\i} norm. We compare it to the fractional Sobolev space obtained by the $K-$method in…

We study the number of (set-theoretically) defining equations of Segre products of projective spaces times certain projective hypersurfaces, extending results by Singh and Walther. Meanwhile, we prove some results about the cohomological…

A basic problem in the theory of partially ordered vector spaces is to characterise those cones on which every order-isomorphism is linear. We show that this is the case for every Archimedean cone that equals the inf-sup hull of the sum of…

In this paper we construct a linear space that parameterizes all invariant bilinear forms on a given vertex algebra with values in a arbitrary vector space. Also we prove that every invariant bilinear form on a vertex algebra is symmetric.…