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2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthorDavid_Corfield
   • CommentTimeJul 31st 2016
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexStarted [[topologically cyclic group]], as needed at [[global family]].

   Started topologically cyclic group, as needed at global family.

2. • CommentRowNumber2.
   • CommentAuthorDavidRoberts
   • CommentTimeJul 31st 2016
   • (edited Jul 31st 2016)
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   Author: DavidRoberts
   Format: MarkdownItex(never mind)

   (never mind)

3. • CommentRowNumber3.
   • CommentAuthorfastlane69
   • CommentTimeAug 1st 2016
   • (edited Aug 1st 2016)
   • PermaLink
   Author: fastlane69
   Format: MarkdownItexDoes a topological cyclic group retain the meaning of a cyclic group as having only one-generator? Or can we have, for example, a free group on 2-generators that is "topologically cyclic" if we can map it to a circle?

   Does a topological cyclic group retain the meaning of a cyclic group as having only one-generator?

   Or can we have, for example, a free group on 2-generators that is “topologically cyclic” if we can map it to a circle?

4. • CommentRowNumber4.
   • CommentAuthorDavid_Corfield
   • CommentTimeAug 1st 2016
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexThe one generator subgroup must be dense. Think of an irrational in $\mathbb{R}/\mathbb{Z}$ under addition.

   The one generator subgroup must be dense. Think of an irrational in $\mathbb{R}/\mathbb{Z}$ under addition.

5. • CommentRowNumber5.
   • CommentAuthorTodd_Trimble
   • CommentTimeAug 1st 2016
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   Author: Todd_Trimble
   Format: MarkdownItexOr even any torus: if you pick a point in $\mathbb{R}^n/\mathbb{Z}^n$ whose coordinates are sufficiently linearly independent, then the closure of the orbit under the $\mathbb{Z}$-action will be dense in the torus.

   Or even any torus: if you pick a point in $\mathbb{R}^n/\mathbb{Z}^n$ whose coordinates are sufficiently linearly independent, then the closure of the orbit under the $\mathbb{Z}$-action will be dense in the torus.