Related papers: Reasonable non--Radon--Nikodym ideals

We study the isomorphism relation on Borel classes of locally compact Polish metric structures. We prove that isomorphism on such classes is always classifiable by countable structures (equivalently: Borel reducible to graph isomorphism),…

We show that some derived $\mathrm{L}^1$ full groups provide examples of non simple Polish groups with the topological bounded normal generation property. In particular, it follows that there are Polish groups with the topological bounded…

Given a Lie group $G$ with finitely many components and a compact Lie group A which acts on $G$ by automorphisms, we prove that there always exists an A-invariant maximal compact subgroup K of G, and that for every such K, the natural map…

A group homomorphism eta:H-->G is called a localization of H if every homomorphism phi:H-->G can be `extended uniquely' to a homomorphism Phi:G-->G in the sense that Phi eta=phi. Libman showed that a localization of a finite group need not…

We discuss when a unital homomorphism {\phi} : C(X) \rightarrow A can be approximated by finite-dimensional homomorphisms, where X is a compact metric space and A is unital simple C*-algebra with tracial rank one. In this paper, we will…

We study the complexity of the isomorphism relation for various classes of closed subgroups of the group of permutations of the natural numbers. We use the setting of Borel reducibility between equivalence relations on Polish spaces. For…

In this paper, we initiate the study of pro-Lie Polish abelian groups from the perspective of homological algebra. We extend to this context the type-decomposition of locally compact Polish abelian groups of Hoffmann and Spitzweck, and…

For a locally finite connected graph $X$ we consider the group $Maps(X)$ of proper homotopy equivalences of $X$. We show that it has a natural Polish group topology, and we propose these groups as an analog of big mapping class groups. We…

Let $K$ be a $p$-adically closed field and $G$ a group interpretable in $K$. We show that if $G$ is definably semisimple (i.e. $G$ has no definable infinite normal abelian subgroups) then there exists a finite normal subgroup $H$ such that…

We show that the regularity of monomial ideals whose associated prime ideals are totally ordered by inclusion is linearly bounded.

In a compact abelian group $X$, a characterized subgroup is a subgroup $H$ such that there exists a sequence of characters $\vs=(v_n)$ of $X$ such that $H=\{x\in X:v_n(x)\to 0 \text{ in } \T\}$. Gabriyelyan proved for $X=\T$, that…

Let $R$ be a polynomial ring in finitely many variables over the integers, and fix an ideal $I$ of $R$. We prove that for all but finitely prime integers $p$, the Bockstein homomorphisms on local cohomology, $H^k_I(R/pR)\to…

A topological group G is profinite if it is compact and totally disconnected. Equivalently, G is the inverse limit of a surjective system of finite groups carrying the discrete topology. We discuss how to represent a countably based…

The Hurewicz property is a classical generalization of $\sigma$-compactness and Sierpi\'nski sets (whose existence follows from CH) are standard examples of non-$\sigma$-compact Hurewicz spaces. We show, solving a problem stated by Szewczak…

It follows from the Garloff-Wagner Theorem that the set of stable polynomials of degree $n$, denoted by $\mathcal{H}_n$, i.e., those whose zeros all lie in the open left complex half-plane, with the Hadamard product $*$, forms an abelian…

We offer a complete classification of right coideal subalgebras which contain all group-like elements for the multiparameter version of the quantum group $U_q(\mathfrak{sl}_{n+1})$ provided that the main parameter $q$ is not a root of 1. As…

We count the number of strictly positive $B$-stable ideals in the nilradical of a Borel subalgebra and prove that the minimal roots of any $B$-stable ideal are conjugate by an element of the Weyl group to a subset of the simple roots. We…

For every countable abelian group $G$ we find the set of all its subgroups $H$ ($H\leq G$) such that a typical measure-preserving $H$-action on a standard atomless probability space $(X,\mathcal{F}, \mu)$ can be extended to a free…

With every $\sigma$-ideal $I$ on a Polish space we associate the $\sigma$-ideal $I^*$ generated by the closed sets in $I$. We study the forcing notions of Borel sets modulo the respective $\sigma$-ideals $I$ and $I^*$ and find connections…

Let $k$ be a totally real field, and let $A/k$ be an absolutely irreducible, polarized Abelian variety of odd, prime dimension whose endomorphisms are all defined over $k$. Then the only strictly compatible families of abstract, absolutely…