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A topological group is a group $G$ together with a topology on the elements of $G$ such that the group operation and group inverse function are both continuous (with respect to the topology).

2 votes

Pontryagin-reflexivity of spaces of continuous functions

This is a bit tangential to your query but I hope that it might be useful. The duality for Banach spaces that you mention is, in my opinion, best expressed in terms of the symmetric one between betwe …
memorial's user avatar
  • 406
1 vote

Parametrization of topological algebraic objects

Please regard this as a tentative answer since I am not sure that it corresponds to the spirit of your query. Many of the situations that you use to illustrate your query can be coded by using the co …
memorial's user avatar
  • 406