Generic properties of topological groups

HIGHLIGHTS

• What: To maintain the coherence and clarity of the paper, in § 3.1, the authors provide several definitions and basic observations that were essentially already present. The authors investigate two important classes of topological groups: The authors extend a classical result of B. H. Neumann, H. Simmons, and A. Macintyre on algebraically closed groups and the word problem while the authors explore the generic subgroup structure of a countably infinite discrete group. One of the main goals of this section is to prove that the purely topological property introduced in the following definition is equivalent to and_ . . .
  

   

  

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