Related papers: Semisolid sets and topological measures

There are two definitions of the measurable functional on the topological vector space: as a linear and measurable real-valued function and as a pointwise limit of the sequence of the continious linear functionals. In general case they are…

Recently many papers on cone metric spaces have been appeared, and main topological properties of such spaces have been obtained. A cone metric space is Hausdorff, and first countable, so the topology of it coincides with a topology induced…

Persistent homology is a method for probing topological properties of point clouds and functions. The method involves tracking the birth and death of topological features (2000) as one varies a tuning parameter. Features with short…

An $\omega_1$-compact space is a space in which every closed discrete subspace is countable. We give various general conditions under which a locally compact, $\omega_1$-compact space is $\sigma$-countably compact, i.e., the union of…

In this paper, we present a constructive generalization of metric and uniform spaces by introducing a new class of spaces, called cover spaces. These spaces form a topological concrete category with a full reflective subcategory of complete…

We introduce a topology on the space of all isomorphism types represented in a given class of countable models, and use this topology as an aid in classifying the isomorphism types. This mixes ideas from effective descriptive set theory and…

We study the local Lipschitz one subsets of a finite dimensional space, that is, sets for which there exists a continuous function whose local Lipschitz derivative is the characteristic function of said set. We give a characterization of a…

We introduce the notion of metric semilattice on the metric space and prove the criterion of $\R$-tree as connected geodesic metric space $X$ admitting the partial order, such that $X$ is semilinear metric semilattice. Also we state the…

This paper investigates spaces equipped with a family of metric-like functions satisfying certain axioms. These functions provide a unified framework for defining topology, uniformity, and diffeology. The framework is based on a family of…

We consider an infinite extension $K$ of a local field of zero characteristic which is a union of an increasing sequence of finite extensions. $K$ is equipped with an inductive limit topology; its conjugate $\bar{K}$ is a completion of $K$…

A transfunction is a function which maps between sets of finite measures on measurable spaces. Push-forward operators form one important class of examples of transfunctions and are identified with their respective measurable functions. In…

We show from a categorical point of view that probability measures on certain measurable or topological spaces arise canonically as the extension of probability distributions on countable sets. We do this by constructing probability monads…

We define a notion of a rotund quasi-uniform space and describe a new direct construction of a (right-continuous) quasi-pseudometric on a (rotund) quasi-uniform space. This new construction allows to give alternative proofs of several…

Motivated by the analysis and geometry of metric-measure structures in infinite dimensions, we study the category of extended metric-topological spaces, along with many of its distinguished subcategories (such as the one of compact spaces).…

Compact sets in constructive mathematics capture our intuition of what computable subsets of the plane (or any other complete metric space) ought to be. A good representation of compact sets provides an efficient means of creating and…

Since their introduction by Thurston, measured geodesic laminations on hyperbolic surfaces occur in many contexts. In this survey, we give a generalization of geodesic laminations on surfaces endowed with a half-translation structure,…

This paper introduces the concepts of correlation entropy and local correlation entropy for free semigroup actions on compact metric space, and explores their fundamental properties. Thereafter, we generalize some classical results on…

Microlocal defect functionals (H-measures, H-distributions, semiclassical measures, etc.) are objects which determine, in some sense, the lack of strong compactness for weakly convergent ${\rm L}^p$ sequences. Recently, Luc Tartar…

Building on the recent work of Mushaandja and Olela-Otafudu~\cite{MushaandjaOlela2025} on modular metric topologies, this paper investigates extended structural properties of modular (pseudo)metric spaces. We provide necessary and…

We develop a folding approach to study two-dimensional symmetry-enriched topological (SET) phases with the mirror reflection symmetry. Our folding approach significantly transforms the mirror SETs, such that their properties can be…