On transversal group topologies

DOI10.1016/j.topol.2005.01.011zbMath1114.22001OpenAlexW2025669264MaRDI QIDQ818403

Dikran Dikranjan, Mikhail G. Tkachenko, I. V. Yaschenko

Publication date: 20 March 2006

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

Full work available at URL: https://doi.org/10.1016/j.topol.2005.01.011

zbMATH Keywords

locally compact abelian groupcentral subgroupprecompact setssubmaximal topologyTransversal topology

Mathematics Subject Classification ID

Structure of general topological groups (22A05) Topological groups (topological aspects) (54H11) Cardinality properties (cardinal functions and inequalities, discrete subsets) (54A25) Counterexamples in general topology (54G20) Consistency and independence results in general topology (54A35)

Related Items

On transversal group topologies ⋮ Counting maximal topologies on countable groups and rings ⋮ Transversal, \(T_{1}\)-independent, and \(T_{1}\)-complementary topologies ⋮ Gaps in the lattices of topological group topologies ⋮ Transversal group topologies on non-Abelian groups ⋮ Transversality on locally pseudocompact groups ⋮ Transversal, \(T_1\)-independent, and \(T_1\)-complementary paratopological group topologies ⋮ Gaps in lattices of (para)topological group topologies and cardinal functions ⋮ Lower continuous topological groups ⋮ Predecessors of topologies of LCA groups ⋮ Independent group topologies on abelian groups

Cites Work

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• On transversal group topologies
• Compactness and connectedness in topological groups
• Independent group topologies on abelian groups
• Some topological groups with and some without suitable sets
• Minimal topological groups
• A characterization of compact or local compact abelian groups in the natural topology
• No submaximal topology on a countable set is $\mathbf {T}_{\mathbf {1}}$-complementary
• A compact Hausdorff topology that is a T₁-complement of itself
• Sequential completeness of quotient groups
• Complementation in the Lattice of T 1 -Topologies
• The Lattice of all Topologies is Complemented
• Topologies with $T_1$-complements
• A T 1 -Complement for the Reals
• Zur Bohr-Konvergenz von Folgen.
• T 1 -Complements of T 1 Topologies
• A class of topologies with $T_1$-complements
• Families of Mutually Complementary Topologies
• On the combination of topologies
• On the Characterization of the Lattice of Topologies^*