检索结果-内蒙古大学图书馆

The borel complexity of ideal limit points

TOPOLOGY AND ITS APPLICATIONS 2022年 312卷

作者： He, Xi Zhang, Hang Zhang, Shuguo Sichuan Univ Coll Math 24 South Sect 1Yihuan Rd Chengdu 610065 Sichuan Peoples R China Southwest Jiaotong Univ Sch Math Xipu CampusWest Pk Hitech Zone Chengdu 611756 Sichuan Peoples R China

In this paper we mainly study the borel complexity of ideal limit points, denoted by Lambda(r)(I), in a first countable space. We investigate the connection between complexity of Lambda(r)(I) and properties of the ideal I, and answer an open question. The main results are the following. Fix a sequence r. Then Lambda(r)(I) can be any nonempty subset of ordinary limit points. This answers an open question. Moreover, under suitable assumptions, if the subset is borel, then the corresponding ideal can be chosen to be borel. Lambda(r)(I) is closed for every real sequence r if and only if I is P+. Lambda(r)(I) is F-sigma for Farah ideals (a subclass of F-sigma delta ideals). These generalize several results in [1]. (c) 2022 Elsevier B.V. All rights reserved.

关键词： Ideal limit points Ideal cluster points borel ideal borel complexity Farah ideal

来源：评论

学校读者我要写书评

暂无评论

borel complexity and automorphisms of C*-algebras

引用

JOURNAL OF FUNCTIONAL ANALYSIS 2015年第12期268卷 3767-3789页

作者： Kerr, David Lupini, Martino Phillips, N. Christopher Texas A&M Univ Dept Math College Stn TX 77843 USA Dept Math & Stat Toronto ON M3J 1P3 Canada Fields Inst Toronto ON M5T 3J1 Canada Univ Oregon Dept Math Eugene OR 97403 USA Univ Toronto Dept Math Toronto ON M5S 2E4 Canada

We show that if A is Z, O-2, O-infinity, a UHF algebra of infinite type, or the tensor product of a UHF algebra of infinite type and O-infinity, then the conjugation action Aut(A) curved right arrow Aut(A) is generically turbulent for the point-norm topology. We moreover prove that if A is either (i) a separable C*-algebra which is stable under tensoring with Z or K, or (ii) a separable Hi factor which is McDuff or a free product of II1 factors, then the automorphisms of A are not classifiable up to conjugacy by countable structures. (C) 2015 Elsevier Inc. All rights reserved.

关键词： Automorphisms C*-algebras II1 factors borel complexity

来源：评论

学校读者我要写书评

暂无评论

MOST(?) THEORIES HAVE borel COMPLETE REDUCTS

引用

JOURNAL OF SYMBOLIC LOGIC 2023年第1期88卷 418-426页

作者： Laskowski, Michael C. Ulrich, Douglas S. Univ Maryland Dept Math College Pk MD 20742 USA

We prove that many seemingly simple theories have borel complete reducts. Specifically, if a countable theory has uncountably many complete one-types, then it has a borel complete reduct. Similarly, if Th(M) is not small, then M(eq )has a borel complete reduct, and if a theory T is not omega-stable, then the elementary diagram of some countable model of T has a borel complete reduct.

关键词： borel complexity countable models reducts

来源：评论

学校读者我要写书评

暂无评论

On the complete metrisability of spaces of contractive semigroups

引用

ARCHIV DER MATHEMATIK 2022年第5期118卷 509-528页

作者： Dahya, Raj Univ Leipzig Fak Math & Informat Augustuspl 10 D-04109 Leipzig Germany

The space of unitary C-0-semigroups on a separable infinite-dimensional Hilbert space, when viewed under the topology of uniform weak operator convergence on compact subsets of R+, is known to admit various interesting residual subspaces. Before treating the contractive case, the problem of the complete metrisability of this space was raised in [4]. Utilising borel complexity computations and automatic continuity results for semigroups, we obtain a general result, which in particular implies that the one-/multiparameter contractive C-0-semigroups constitute Polish spaces and thus positively addresses the open problem.

关键词： Semigroups of operators Metrisability Completeness Polish spaces borel complexity

来源：评论

学校读者我要写书评

暂无评论

Descriptive complexity of topological invariants

引用

ANNALS OF PURE AND APPLIED LOGIC 2025年第8期176卷

作者： Amir, Djamel Eddine Hoyrup, Mathieu Univ Lorraine CNRS Inria LORIA F-54000 Nancy France

In this article, we investigate the descriptive complexity of topological invariants. Our main goal is to understand the expressive power of low complexity invariants, by investigating which spaces they can distinguish. We study the invariants in the first two levels of the borel hierarchy. We develop techniques to establish whether two spaces can be separated by invariants in these levels. We show that they are sufficient to separate finite topological graphs. We finally identify the complexity of recognizing the line segment. (c) 2025 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

关键词： Computable analysis Descriptive set theory Topology Topological invariant borel complexity

来源：评论

学校读者我要写书评

暂无评论

(Looking for) the heart of abelian Polish groups

引用

ADVANCES IN MATHEMATICS 2024年 453卷

作者： Lupini, Martino Univ Bologna Dipartimento Matemat Piazza Porta S Donato 5 I-40126 Bologna Italy

We prove that the category M of abelian groups with a Polish cover introduced in collaboration with Bergfalk and Panagiotopoulos is the left heart of (the derived category of) the quasi-abelian category A of abelian Polish groups in the sense of Beilinson-Bernstein-Deligne and Schneiders. Thus, M is an abelian category containing A as a full subcategory such that the inclusion functor A-* M is exact and finitely continuous. Furthermore, M is uniquely characterized up to equivalence by the following universal property: for every abelian category B, a functor A-* B is exact and finitely continuous if and only if it extends to an exact and finitely continuous functor M-* B. In particular, this provides a description of the left heart of A as a concrete category. We provide similar descriptions of the left heart of a number of categories of algebraic structures endowed with a topology, including: non-Archimedean abelian Polish groups;locally compact abelian Polish groups;totally disconnected locally compact abelian Polish groups;Polish R-modules, for a given Polish group or Polish ring R;and separable Banach spaces and separable Fr & eacute;chet spaces over a separable complete nonArchimedean valued field. (c) 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons .org /licenses /by /4 .0/).

关键词： Abelian Polish group Quasi-abelian category Abelian category Left heart borel complexity

来源：评论

学校读者我要写书评

暂无评论

Some applications of the theory of Katetov order to ideal convergence

引用

TOPOLOGY AND ITS APPLICATIONS 2021年 301卷 107545-107545页

作者： Zhang, Hang Zhang, Shuguo Southwest Jiaotong Univ Sch Math Chengdu 610756 Peoples R China Sichuan Univ Coll Math Chengdu 610064 Peoples R China

In this paper we establish connections between the theory of Katetov order on ideals on countable sets with ideal convergence in general topological spaces, which are used to study the following questions posed by X.G. Zhou, L. Liu and S. Lin [12]: (1) Whether every finite union of I-closed subsets is I-closed? (2) Must every I-continuous map preserve I-convergence? (3) Must every map preserving I-convergence preserve J-convergence if J subset of I? Our main results include: If I is K-uniform, then every finite union of I-closed subsets is I-closed in any space;there exists a countable zero-dimensional Hausdorff space with character equal to the continuum in which there are two I-closed sets with non-I-closed union for some tall F-sigma-ideal I, while it is independent of ZFC that for every Hausdorff space X of character less than the continuum and every tall F-sigma-ideal I, finite unions of I-closed subsets are always I-closed in X. These answers Question (1). We show the answer to Question (2) is negative in ZFC and the answer to Question (3) is also negative if we replace J subset of I with J <=(K) I (which is weaker than J subset of I). (C) 2020 Elsevier B.V. All rights reserved.

关键词： Ideal convergence I-closed borel complexity Katetov order K-uniform

来源：评论

学校读者我要写书评

暂无评论

Conjugacy for homogeneous ordered graphs

引用

ARCHIVE FOR MATHEMATICAL LOGIC 2019年第3-4期58卷 457-467页

作者： Coskey, Samuel Ellis, Paul Boise State Univ Dept Math 1910 Univ Dr Boise ID 83725 USA Manhattanville Coll Dept Math & Comp Sci 2900 Purchase St Purchase NY 10577 USA

We show that for any countable homogeneous ordered graph G, the conjugacy problem for automorphisms of G is borel complete. In fact we establish that each such G satisfies a strong extension property called ABAP, which implies that the isomorphism relation on substructures of G is borel reducible to the conjugacy relation on automorphisms of G.

关键词： Conjugacy Homogeneous structure borel complexity Ordered graphs

来源：评论

学校读者我要写书评

暂无评论

Generating new ideals using weighted density via modulus functions

引用

INDAGATIONES MATHEMATICAE-NEW SERIES 2018年第5期29卷 1196-1209页

作者： Bose, Kumardipta Das, Pratulananda Kwela, Adam Jadavpur Univ Dept Math Kolkata 700032 India Univ Gdansk Inst Math Fac Math Phys & Informat Ul Wita Stwosza 57 PL-80308 Gdansk Poland

In this paper we extend the idea of weighted density of Balcerzak et al. (2015) by using a modulus function and introduce the idea f -density of weight g of subsets of omega := {0,1, ...} (at the same time extending the notion of f-density (Aizpuru et al., 2014)), which we name d(g)(f) where g : omega -> [0, infinity) satisfies g(n) -> infinity and n/g(n) -> 0 and f is a modulus function. The aim of this paper is to show that we can get new ideals Z(g)(f) consisting of sets A subset of omega co for which d(g)(f) (A) = 0 different from all the previously constructed ideals Z(g) (f) of Balcerzak et al. (2015) and moreover they retain all the nice properties of the ideals Z(g). (C) 2018 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.

关键词： Generalized density Weight function Modulus function P-ideal Density ideal borel complexity

来源：评论

学校读者我要写书评

暂无评论

THE CLASSIFICATION PROBLEM FOR OPERATOR ALGEBRAIC VARIETIES AND THEIR MULTIPLIER ALGEBRAS

引用

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY 2018年第3期370卷 2161-2180页

作者： Hartz, Michael Lupini, Martino Univ Waterloo Dept Pure Math Waterloo ON N2L 3G1 Canada Washington Univ Dept Math One Brookings Dr St Louis MO 63130 USA Univ Vienna Fak Math Oskar Morgenstern Pl 1Room 02-126 A-1090 Vienna Austria CALTECH Dept Math 1200 E Calif BlvdMC 253-37 Pasadena CA 91125 USA

We study from the perspective of borel complexity theory the classification problem for multiplier algebras associated with operator algebraic varieties. These algebras are precisely the multiplier algebras of irreducible complete Nevanlinna-Pick spaces. We prove that these algebras are not classifiable up to algebraic isomorphism using countable structures as invariants. In order to prove such a result, we develop the theory of turbulence for Polish groupoids, which generalizes Hjorth's turbulence theory for Polish group actions. We also prove that the classification problem for multiplier algebras associated with varieties in a finite-dimensional ball up to isometric isomorphism has maximum complexity among the essentially countable classification problems. In particular, this shows that Blaschke sequences are not smoothly classifiable up to conformal equivalence via automorphisms of the disc.

关键词： Non-selfadjoint operator algebra reproducing kernel Hilbert space multiplier algebra Nevanlinna-Pick kernel borel complexity turbulence Polish groupoid Blaschke sequence

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：