Related papers: $L'$-localization in an $\infty$-topos

For $a\in [0,+\infty)$, the function space $E_{\geq a}$ ($E_{>a}$; $E_{\leq a}$; $E_{<a}$) of all continuous maps from $[0,1]$ to itself whose topological entropies are larger than or equal to $a$ (larger than $a$; smaller than or equal to…

We show via an application of techniques from complex interpolation theory how the $L^p$-pseudofunction algebras of a locally compact group $G$ can be understood as sitting between $L^1(G)$ and $C^*(G)$. Motivated by this, we collect and…

We consider topological conditions under which a locally invertible map admits a global inverse. Our main theorem states that a local diffeomorphism $f: M \to\mathbb{R}^n$ is bijective if and only if $H_{n-1}(M)=0$ and the pre-image of…

In this paper, local monomialization theorems are proven for analytic morphisms of complex and real analytic spaces. This gives the generalization of the local monomialization theorem for morphisms of algebraic varieties over a field of…

We introduce and investigate using Hilbert modules the properties of the {\em Fourier algebra} $A(G)$ for a locally compact groupoid $G$. We establish a duality theorem for such groupoids in terms of multiplicative module maps. This…

It is shown that the algebra \(L^\infty(\mu)\) of all bounded measurable functions with respect to a finite measure \(\mu\) is localizing on the Hilbert space \(L^2(\mu)\) if and only if the measure \(\mu\) has an atom. Next, it is shown…

We study phenomena where some eigenvectors of a graph Laplacian are largely confined in small subsets of the graph. These localization phenomena are similar to those generally termed Anderson Localization in the Physics literature, and are…

An extended derivation (endomorphism) of a (restricted) Lie algebra $L$ is an assignment of a derivation (respectively) of $L'$ for any (restricted) Lie morphism $f:L\to L'$, functorial in $f$ in the obvious sense. We show that (a) the only…

We show that the category $L\textbf{-Top}_{0}$ of $T_{0}$-$L$-topological spaces is the epireflective hull of Sierpinski $L$-topological space in the category $L\textbf{-Top}$ of $L$-topological spaces and the category $L\textbf{-Sob}$ of…

We study the problem of topologically order-embedding a given topological poset X in the space of all closed subsets of X which is topologized by the Fell topology and ordered by set inclusion. We show that this can be achieved whenever X…

Let $L^{m,p}(\R^n)$ denote the Sobolev space of functions whose $m$-th derivatives lie in $L^p(\R^n)$, and assume that $p>n$. For $E \subset \R^n$, denote by $L^{m,p}(E)$ the space of restrictions to $E$ of functions $F \in L^{m,p}(\R^n)$.…

The interaction of a Lie algebra $\LL,$ having a weight space decomposition with respect to a nonzero toral subalgebra, with its corresponding root system forms a powerful tool in the study of the structure of $\LL.$ This, in particular,…

Localization of electronic wave functions in modern two-dimensional (2D) materials such as graphene can impact drastically their transport and magnetic properties. The recent localization landscape (LL) theory has brought many tools and…

We characterize the class of homotopy pull-back squares by means of elementary closure properties. The so called Puppe theorem which identifies the homotopy fiber of certain maps constructed as homotopy colimits is a straightforward…

We introduce locally involutive semigroups and embed them into the category of ordered groupoids. This embedding restricts to a correspondence between quasi-involutive semigroups and ordered groupoids with mediator, extending the classical…

This note provides some technical support to the proof of a result of W. Winter which shows that two unital separable simple amenable ${\cal Z}$-absorbing C*-algebras with locally finite decomposition property satisfying the UCT whose…

Photonic topological insulators exhibit bulk-boundary correspondence, which requires that boundary-localized states appear at the interface formed between topologically distinct insulating materials. However, many topological photonic…

By using a lattice characterization of continuous projections defined on a topological vector space E arising from a dual pair, we determine the automorphism group of their orthomodular poset Proj(E) by means of automorphisms and…

In this paper, we relate Lie algebroids to Costello's version of derived geometry. For instance, we show that each Lie algebroid $L$-and the natural generalization to dg Lie algebroids-provides an (essentially unique) $L_\infty$ space. More…

We consider Walsh's conformal map from the complement of a compact set $E = \cup_{j=1}^\ell E_j$ with $\ell$ components onto a lemniscatic domain $\widehat{\mathbb{C}} \setminus L$, where $L$ has the form $L = \{ w \in \mathbb{C} :…