Related papers: Representations and Semisimplicity of Ordered Topo…

Given a strictly positive measure, we characterize inner semicontinuous solid convex-valued mappings for which continuous functions which are selections almost everywhere are selections. This class contains continuous mappings as well as…

Pre-trained large foundation models play a central role in the recent surge of artificial intelligence, resulting in fine-tuned models with remarkable abilities when measured on benchmark datasets, standard exams, and applications. Due to…

Generally-unbounded infinitesimal generators are studied in the context of operator topology. Beginning with the definition of seminorm, the concept of locally convex topological vector space is introduced as well as the concept of…

We define the notion of {\em rational presentation of a complete metric space} in order to study metric spaces from the algorithmic complexity point of view. In this setting, we study some presentations of the space $\czu$ of uniformly…

The concept of quasi-partial b-metric-like spaces is being introduced and studied with the help of topology. Examples are also discussed to support the results. Some fixed point theorems are proved in the setting of quasi-partial…

In the case of an ordered vector space with an order unit, the Archimedeanization method has been developed recently by V.I Paulsen and M. Tomforde. We present a general version of the Archimedeanization which covers arbitrary ordered…

We define and prove some properties of the semi-classical wavefront set. We also define and study semi-classical Fourier integral operators, of which we give a complete characterization. Lastly, we prove a generalization of the…

Some zeta functions which are naturally attached to the locally homogeneous vector bundles over compact locally symmetric spaces of rank one are investigated. We prove that such functions can be expressed in terms of entire functions whose…

Reeb spaces of real-valued functions on manifolds are the spaces of all connected components (contours) of level sets and endowed with the natural quotient topology. They have been fundamental and strong tools in investigating manifolds via…

Exact indecomposable module categories over the tensor category of representations of Hopf algebras that are liftings of quantum linear spaces are classified.

We study topological boundedness of order-to-topology bounded and order-to-topology continuous operators from ordered vector spaces to topological vector spaces. The uniform boundedness principle for such operators is investigated.

We give a complete classification in canonical forms on finite-dimensional vector spaces over the real numbers.

In this paper, the class of (complex) quasi-Herglotz functions is introduced as the complex vector space generated by the convex cone of ordinary Herglotz functions. We prove characterization theorems, in particular, an analytic…

Let $\precsim$ be a reflexive binary relation on a topological space $(X, \tau )$. A pair $(u,v)$ of continuous real-valued functions on $(X, \tau )$ is said to be a {\em continuous representation} of $\precsim$ if, for all $x,y \in X$,…

Condensed mathematics, developed by Clausen and Scholze over the last few years, proposes a generalization of topology with better categorical properties. It replaces the concept of a topological space by that of a condensed set, which can…

For a field $\ef$, the discrete topological vector spaces over $\ \ef$ are essentially of the form $\ef^{\alpha}$ where $\alpha$ is an ordinal. With additional appropriate properties, they are isomorphic to $\ef^{(\beta)}$ where $\beta$ is…

In this paper, we study the topology of ordered Hurwitz space. These are moduli spaces of branched covers with a choice of ordering on the branched points. Answering a question of Ellenberg, we prove that the homology of ordered Hurwitz…

We give several characterizations of order continuous vector lattice homomorphisms between Archimedean vector lattices. We reduce the proofs of some of the equivalences to the case of composition operators between vector lattices of…

In this paper we will study the representations of isomorphisms between bases of topological spaces. It turns out that the perfect setting for this study is that of regular open subsets of complete metric spaces, but we have achieved some…

26 different concrete representations of the space of vector valued distributions on a smooth manifold of dimension n are presented systematically, most of them new. In the particular case of representations as module homomorphisms acting…