Related papers: A counterexample regarding an equivalence relation…

In this paper we propose counterexamples to the Geometrization Conjecture and the Elliptization Conjecture.

The following will be shown: Let $I$ be a $\sigma$-ideal on a Polish space $X$ with the property that the associated forcing of $I^+$ Borel subsets ordered by $\subseteq$ is a proper forcing. Let E be an analytic or coanalytic equivalence…

We provide new simple proofs of the Kolmogorov extension theorem and Prokhorovs' theorem. The proof of the Kolmogorov extension theorem is based on the simple observation that $\mathbb{R}$ and the product measurable space…

We give the counter-examples related to a Gaussian Brunn-Minkowski inequality and the (B) conjecture.

Coskey, Hamkins, and Miller [CHM12] proposed two possible analogues of the class of countable Borel equivalence relations in the setting of computable reducibility of equivalence relations on the computably enumerable (c.e.) sets. The first…

We provide a proof and a counterexample to two conjectures made by N. Kuznetsov.

A counterpart of the famous Bessel's inequality for orthornormal families in real or complex inner product spaces is given. Applications for some Gruss type inequalities are also provided.

For a finite-dimensional Lie algebra $\mathfrak g$ over a field $\mathbb K\supset \mathbb C$, we deduce from the compatibility between cup products Kontsevich (2003, Section 8) and from the main result of Shoikhet (2001) an alternative way…

The class of spaces such that their product with every Lindel\"of space is Lindel\"of is not well-understood. We prove a number of new results concerning such productively Lindel\"of spaces with some extra property, mainly assuming the…

General considerations on the Equivalence conjectures and a review of few mathematical results.

In this note we give a counterexample to a conjecture proposed by Ciliberto about special linear systems of P^n through multiple base points.

In this note we prove a converse of Bohr's equivalence theorem for Dirichlet series under some natural assumptions.

We prove an analogue of the portmanteau theorem on weak convergence of probability measures allowing measures which are unbounded on an underlying metric space but finite on the complement of any Borel neighbourhood of a fixed element.

We discuss a construction that gives counterexamples to various questions of unique determination of convex bodies.

We prove that Sobolev spaces on Cartesian and warped products of metric spaces tensorize, only requiring that one of the factors is a doubling space supporting a Poincar\'e inequality.

A Borel equivalence relation on a Polish space is said to be countable if all of its equivalence classes are countable. Standard examples of countable Borel equivalence relations (on the space of subsets of the integers) that occur in…

The study of Borel equivalence relations under Borel reducibility has developed into an important area of descriptive set theory. The dichotomies of Silver and Harrington-Kechris-Louveau show that with respect to Borel reducibility, any…

We show that if an equivalence relation $E$ on a Polish space is a countable union of smooth Borel subequivalence relations, then there is either a Borel reduction of $E$ to a countable Borel equivalence relation on a Polish space or a…

We show that the unitary conjugacy relation for unitary representations of a second countable locally compact group on a separable Hilbert space is a Borel equivalence relation.

Some related results to Pecaric's inequality in inner product spaces that generalises Bombieri's inequality, are given.