Related papers: Urysohn Lemmas in Topological Vector Spaces

Using classical results of infinite-dimensional geometry, we show that the isometry group of the Urysohn space, endowed with its usual Polish group topology, is homeomorphic to the separable Hilbert space. The proof is basedon a lemma about…

In this paper, we completely classify conformal solitons on pseudo-Riemannian hypersurfaces in pseudo-Euclidean spaces arisen from the position vector field. In particular, the classification of Yamabe solitons on pseudo-Riemannian…

We use quantum and Floer homology to construct (partial) quasi-morphisms on the universal cover of the group of compactly supported Hamiltonian diffeomorphisms for a certain class of non-closed strongly semi-positive symplectic manifolds…

We show that complex geometric features of Teichmuller spaces create explicitly the extremals of generic homogeneous holomorphic functionals on univalent functions. In particular this gives proofs of the well-known Zalcman and Bieberbach…

We provide base change theorems, projection formulae and Verdier duality for both cohomology and homology in the context of finite topological spaces

We define a universal Teichm\"uller space for locally quasiconformal mappings whose dilatation grows not faster than a certain rate. Paralleling the classical Teichm\"uller theory, we prove results of existence and uniqueness for extremal…

We construct a topological invariant that classifies density matrices of symmetry-protected topological orders in two-dimensional fermionic systems. As it is constructed out of the previously introduced Uhlmann phase, we refer to it as the…

In this paper, we consider certain topological properties along with certain types of mappings on these spaces defined by the notion of ideal convergence. In order to do that, we primarily follow in the footsteps of the earlier studies of…

There exist several interesting results in the literature on subnormal operator tuples having their spectral properties tied to the geometry of strictly pseudoconvex domains or to that of bounded symmetric domains in $\C^n$. We introduce a…

We introduce functional Wulff shapes based on the classical construction for compact convex sets. With this new tool, we establish a functional version of Aleksandrov's variational lemma in the family of convex functions with compact…

A topological space is $Suslin$ ($Lusin$) if it is a continuous (and bijective) image of a Polish space. For a Tychonoff space $X$ let $C_p(X)$, $C_k(X)$ and $C_{{\downarrow}F}(X)$ be the space of continuous real-valued functions on $X$,…

Ordered locally convex spaces is an important classes of spaces in the theory of ordered topological vector spaces just as locally convex spaces in the theory of topological vector spaces. Some special classes of ordered locally convex…

We study the topology of a class of proper submodules and some of its distinguished subclasses and call them structure spaces. We give several criteria for the quasi-compactness of these structure spaces. We study $T_0$ and $T_1$ separation…

We construct in ZFC an L topological vector space -- a topological vector space that is an L space -- and an L field -- a topological field that is an L space. This generalizes results in [5] and [8].

Any symmetric affinity function $w: V\times V \to \mathbb{R}_+$ defined on a discrete set $V$ induces Euclidean space structure on $V$. In particular, an undirected graph specified by an affinity (or adjacency) matrix can be considered as a…

In the theory of Teichm\"uller space of Riemann surfaces, we consider the set of Riemann surfaces which are quasiconformally equivalent. For topologically finite Riemann surfaces, it is quite easy to examine if they are quasiconformally…

Convex sets appear in various mathematical theories, and are used to define notions such as convex functions and hulls. As an abstraction from the usual definition of convex sets in vector spaces, we formalize in Coq an intrinsic…

The main goal of this paper is to study the topological properties of tensors in tree-based Tucker format. These formats include the Tucker format and the Hierarchical Tucker format. A property of the so-called minimal subspaces is used for…

In this paper, we construct compact embedded $\lambda$-hypersurfaces with the topology of torus which are called $\lambda$-torus in Euclidean spaces $\mathbb {R}^{n+1}$.

We shown that every continuous local functional on the space of finite convex functions on $\mathbb{R}^n$ is a valuation. This relation is used to establish a homogeneous decomposition for the class of polynomial local functionals as well…