Automorphism groups of dense subgroups of \(\mathbb{R}^n\)

DOI10.1016/j.topol.2019.107000zbMath1443.22003arXiv1912.04668OpenAlexW2995350875MaRDI QIDQ1985625

Vitalij A. Chatyrko, Dmitrij B. Shakhmatov

Publication date: 7 April 2020

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1912.04668

zbMATH Keywords

automorphism groupalgebraic numberfinite-dimensional vector spacetranscendental field extensioncomplete topological vector spacedense subgroup of \(\mathbb{R}^n\)general linear group \(G L(n,\mathbb{R})\)Laurent polynomial with integer coefficientsorthogonal group \(O(n)\)special linear group \(SL(n)\)special orthogonal group \(SO(n)\)

Mathematics Subject Classification ID

Structure of general topological groups (22A05) Group rings (16S34) Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.) (46A16) Topological groups (topological aspects) (54H11) Groups and semigroups of linear operators (47D03) Automorphisms of abstract finite groups (20D45) Automorphisms of infinite groups (20E36) Dimension theory in general topology (54F45) Algebraic numbers; rings of algebraic integers (11R04) Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups (20K30) Topological fields, rings, etc. (topological aspects) (54H13) Transcendental field extensions (12F20) Orthogonal and unitary groups in metric geometry (51F25)

Related Items (1)

On subsets of \(\mathbb{R}^n\) spanning it via positive integers as multipliers

Cites Work

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• Topological groups and related structures
• The structure of compact groups. A primer for the student -- A handbook for the expert
• Weight of closed subsets topologically generating a compact group

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