Mackey groups and Mackey topologies

DOI10.4064/dm835-7-2021OpenAlexW3211726889WikidataQ114021998 ScholiaQ114021998MaRDI QIDQ5029009

Dikran Dikranjan, Lydia Außenhofer

Publication date: 11 February 2022

Published in: Dissertationes Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4064/dm835-7-2021

Mathematics Subject Classification ID

Structure of general topological groups (22A05) Topological groups (topological aspects) (54H11) Baire category, Baire spaces (54E52) Logical aspects of lattices and related structures (03G10) Unitary representations of locally compact groups (22D10) General theory of locally convex spaces (46A03) Algebraic properties of function spaces in general topology (54C40) General properties and structure of locally compact groups (22D05) Barrelled spaces, bornological spaces (46A08) Lattices of continuous, differentiable or analytic functions (46E05) Duality theorems for locally compact groups (22D35) Algebraic aspects of posets (06A11) General properties and structure of LCA groups (22B05) Homological and categorical methods for abelian groups (20K40) Direct sums, direct products, etc. for abelian groups (20K25) Rings and algebras of continuous, differentiable or analytic functions (46E25) Torsion-free groups, finite rank (20K15) Topological methods for abelian groups (20K45) Character groups and dual objects (43A40)

Related Items (2)

Tameness and Rosenthal type locally convex spaces ⋮ Compatible group topologies on a locally quasi-convex abelian group and the Mackey group problem

Cites Work

• A characterization of barrelledness of \(C_{p}(X)\)
• Topological properties of the group of the null sequences valued in an abelian topological group
• On the set of locally convex topologies compatible with a given topology on a vector space: cardinality aspects
• On the Mackey topology for abelian topological groups and locally convex spaces
• Mackey topology on locally convex spaces and on locally quasi-convex groups. Similarities and historical remarks
• Compact-like abelian groups without non-trivial quasi-convex null sequences
• On the Hausdorff variety generated by all locally \(k_\omega\) groups and on Schwartz groups
• Linear topologies on \(\mathbb Z\) are not Mackey topologies
• \(\mathbb{Q}\) is not a Mackey group
• ``Varopoulos paradigm: Mackey property versus metrizability in topological groups
• Groups of quasi-invariance and the Pontryagin duality
• On quasi-convex null sequences in infinite cyclic groups
• Duality properties of bounded torsion topological abelian groups
• Sur quelques propriétés de l'espace C\(_s\)(T)
• Limits in compact Abelian groups
• Locally compact abelian groups admitting non-trivial quasi-convex null sequences
• Characterizing subgroups of compact Abelian groups
• A complete solution of Markov's problem on connected group topologies
• Countable powers of compact abelian groups in the uniform topology and cardinality of their dual groups
• Topological groups and related structures
• Characterizations of groups generated by Kronecker sets
• Uncountable products of determined groups need not be determined
• Countably infinite quasi-convex sets in some locally compact abelian groups
• Quasi-convex sequences in the circle and the 3-adic integers
• Quasi-convex density and determining subgroups of compact Abelian groups
• Some results on separate and joint continuity
• On the existence of exotic Banach-Lie groups
• Additive subgroups of topological vector spaces
• Topological properties of spaces of continuous functions
• Separate continuity and joint continuity
• Examples of not continuous actions of a group in a compact space
• Open subgroups and Pontryagin duality
• Some properties of locally quasi-convex groups
• Chains of pseudocompact group topologies
• Cardinal invariants and independence results in the poset of precompact group topologies
• Pontryagin duality for metrizable groups
• Answer to Raczkowski's questions on convergent sequences of integers
• Dual properties in totally bounded Abelian groups
• Topologies on the direct sum of topological Abelian groups
• A Mackey-Arens theorem for topological Abelian groups
• The Mackey problem for free locally convex spaces
• A characterization of the maximally almost periodic abelian groups
• On the non-existence of the Mackey topology for locally quasi-convex groups
• Locally pseudocompact topological groups
• Open subgroups, compact subgroups and Binz-Butzmann reflexivity
• On reflexive group topologies on Abelian groups of finite exponent
• Pontryagin duality in the class of precompact abelian groups and the Baire property
• Characterizing sequences for precompact group topologies
• Locally quasi-convex compatible topologies on locally compact abelian groups
• The group \(\mathbb{Z}^{( \mathbb{N})}\) does not have a Mackey topology
• On convergent sequences in dual groups
• The Mackey problem for free abelian topological groups
• On ultrabarrelled spaces, their group analogs and Baire spaces. In honour of Manuel López-Pellicer, loyal friend and indefatigable mathematician
• Maximally almost periodic groups and respecting properties. In honour of Manuel López-Pellicer
• Locally quasi-convex compatible topologies on a topological group
• The Mackey topology problem: a complete solution for bounded groups
• Sequences and filters of characters characterizing subgroups of compact Abelian groups
• Über die Einbettung der nuklearen Räume in \((s)^ A\)
• Characters of locally compact abelian groups
• Pseudocompactness and uniform continuity in topological groups
• On \(g\)-barrelled groups and their permanence properties
• Topological groups with many small subgroups
• A note on weakly compact subgroups of locally quasi-convex groups
• Duality in linear spaces
• Extensions of the Pontrjagin duality. I: Infinite products
• A group-theoretic method in approximation theory
• The Pontrjagin duality theorem in linear spaces
• Zur Dualitätstheorie projektiver Limites abelscher Gruppen
• On local quasi-convexity as a three-space property in topological abelian groups
• Some aspects of nuclear vector groups
• Barely Baire spaces
• Group valued null sequences and metrizable non-Mackey groups
• Quasi-convexly dense and suitable sets in the arc component of a compact group
• The Dual Group of a Dense Subgroup
• Reflection principle characterizing groups in which unconditionally closed sets are algebraic
• On the Glicksberg theorem for locally quasi-convex Schwartz groups
• Sous-groupes de IR liés à la répartition modulo 1 de suites
• Note on Compatible Vector Topologies
• A Convergence Problem Connected with Continued Fractions
• Compactness type properties in topological groups
• Algebraic structure of pseudocompact groups
• Uniform Boundedness for Groups
• The Weight of a Pseudocompact (Homogeneous) Space Whose Cardinality Has Countable Cofinality
• Joint Continuity of Separately Continuous Functions
• FREE TOPOLOGICAL GROUPS OF METRIZABLE SPACES
• Abelian Groups which Satisfy Pontryagin Duality need not Respect Compactness
• Topological Spaces That are α-Favorable for a Player with Perfect Information
• A property of Dunford-Pettis type in topological groups
• A locally quasi-convex abelian group without a Mackey group topology
• SSGP topologies on abelian groups of positive finite divisible rank
• Proper Pseudocompact Extensions of Compact Abelian Group Topologies
• Jeux Topologiques et Espaces de Namioka
• Good approximation and characterization of subgroups of R = Z
• Free Abelian topological groups and the Pontryagin-Van Kampen duality
• COMPATIBLE LOCALLY CONVEX TOPOLOGIES ON NORMED SPACES: CARDINALITY ASPECTS
• Countably compact groups without non-trivial convergent sequences
• Good Approximations and Continued Fractions
• Abelian Groups
• Characteristics of the Mackey Topology for Abelian Topological Groups
• On Schwartz groups
• Some remarks on monothetic groups
• Closed subgroups of locally compact Abelian groups
• Precompact noncompact reflexive Abelian groups
• Locally compact groups and the continuum hypothesis
• Topologies induced by groups of characters
• Connectivity, Divisibility, and Torsion
• A note on the duality of locally compact groups
• Compactness in Hom(G, H)
• k-Groups and Duality
• A remark on characters of locally compact Abelian groups
• On Convex Topological Linear Spaces
• On Convex Topological Linear Spaces
• The structure of compact groups. A primer for the student -- a handbook for the expert
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Mackey groups and Mackey topologies