The space of closed subgroups of \(\mathbb{R}^2\)

DOI10.1016/0040-9383(79)90032-6zbMath0429.57002OpenAlexW2073272070MaRDI QIDQ1137799

John H. Hubbard, Ibrahim Pourezza

Publication date: 1979

Published in: Topology (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0040-9383(79)90032-6

zbMATH Keywords

Hausdorff metricelliptic curveelliptic functionstrefoil knotspace of closed subgroups of 2-space which are not Z+Zspace of closed subgroups of R2

Mathematics Subject Classification ID

General low-dimensional topology (57M99) Special algebraic curves and curves of low genus (14H45) Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) (30F35) Families, moduli of curves (analytic) (14H15) Locally compact abelian groups (LCA groups) (22B99)

Related Items (16)

Connectedness of the space of subgroups ⋮ Distal Actions of Automorphisms of Lie Groups G on Sub_G ⋮ The space of geometric limits of one-generator closed subgroups of \(\text{PSL}_{2}(\mathbb R)\) ⋮ On the Chabauty space of locally compact Abelian groups ⋮ Dynamics of actions of automorphisms of discrete groups \(G\) on \(\mathrm{Sub}_G\) and applications to lattices in Lie groups ⋮ Unnamed Item ⋮ Locally compact groups with totally disconnected space of subgroups ⋮ Asymptotic windings over the trefoil knot ⋮ The space of closed subgroups of \(\mathbb R\times \mathbb Z\) ⋮ Local limits of connected subgroups of \(\mathrm{SL}_3(\mathbb{R})\) ⋮ The Chabauty space of \(\mathbb{Q}_p^\times\) ⋮ Selective survey on spaces of closed subgroups of topological groups ⋮ The space of closed subgroups of ℝⁿis stratified and simply connected ⋮ Expansive actions of automorphisms of locally compact groups \(G\) on \(\text{Sub}_G\) ⋮ DISTAL ACTIONS OF AUTOMORPHISMS OF NILPOTENT GROUPS G ON SUB_G AND APPLICATIONS TO LATTICES IN LIE GROUPS ⋮ ON THE CONNECTEDNESS OF THE CHABAUTY SPACE OF A LOCALLY COMPACT PRONILPOTENT GROUP

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