Related papers: Topological description of the Borel probability s…

The signature of closed oriented manifolds is well-known to be multiplicative under finite covers. This fails for Poincar\'e complexes as examples of C. T. C. Wall show. We establish the multiplicativity of the signature, and more…

While topological data analysis has emerged as a powerful paradigm for structural inference, its foundational tools, notably persistent homology and the persistent Laplacian, are frequently insensitive to localized structural fluctuations…

It is proved that two useful and apparently different metrics on the set of Borel probabilities on countable products of Polish spaces of bounded diameters are equal. This paves the way for advances in their computation.

In this paper we provide a framework for quantitative statements on distances and measures when studying algebraic varieties and morphisms of algebraic varieties over local fields. We will concentrate on local fields of the type…

In this article, we characterize both Lusin's theorem and the existence of Borel representatives via the regularity properties of the measure in general topological measure spaces. As a corollary, we prove that Borel regularity of the…

Light scattering in random media is usually considered within the framework of the three-dimensional Anderson universality class, with modifications for the vector nature of electromagnetic waves. We propose that the linear dispersiveness…

Let $Bo(T,\tau)$ be the Borel $\sigma$-algebra generated by the topology $\tau$ on $T$. In this paper we show that if $K$ is a Hausdorff compact space, then every subset of $K$ is a Borel set if, and only if,…

The conventional definition of a topological metric over a space specifies properties that must be obeyed by any measure of "how separated" two points in that space are. Here it is shown how to extend that definition, and in particular the…

Let $M$ be an orientable connected closed surface and $f$ be an $R$-closed homeomorphism on $M$ which is isotopic to identity. Then the suspension of $f$ satisfies one of the following condition: 1) the closure of each element of it is…

Recently, Li, Li and Zhang introduced the topological pressure for correspondences and measure-theoretic entropy for transition probability kernels. Building thereon, they established a variational principle for correspondences satisfying…

Let $C$ be an open cone in a Banach space equipped with the Thompson metric with closure a normal cone. The main result gives sufficient conditions for Borel probability measures $\mu,\nu$ on $C$ with finite first moment for which $\mu\leq…

We consider several ways to test for topology directly in harmonic space by comparing the measured a_lm with the expected correlation matrices. Two tests are of a frequentist nature while we compute the Bayesian evidence as the third test.…

We provide a pointwise bipolar theorem for liminf-closed convex sets of positive Borel measurable functions on a sigma-compact metric space without the assumption that the polar is a tight set of measures. As applications we derive a…

In this paper we consider some properties of a space B(X) of Borel functions on a set of reals X, with pointwise topology, that are stronger than separability.

We give, for each level of complexity L, a Hurewicz-like characterization of the Borel subsets with countable sections of a product of two Polish spaces that cannot become in L by changing the two Polish topologies.

First, we generalize the definition of a locally compact topology given by Paterson and Welch for a sequence of locally compact spaces to the case where the underlying spaces are $T_1$ and sober. We then consider a certain semilattice of…

In this paper we present with algebraic trees a novel notion of (continuum) trees which generalizes countable graph-theoretic trees to (potentially) uncountable structures. For that purpose we focus on the tree structure given by the branch…

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…

We show that the spaces of holomorphic and continuous maps from a smooth complex projective variety to a projective space have the same homology in a range depending on the degree of the maps.

The Kantorovich metric provides a way of measuring the distance between two Borel probability measures on a metric space. This metric has a broad range of applications from bioinformatics to image processing, and is commonly linked to the…