Is there somone help me to show that if this problem have positive Answer :
Problem :Can every non-discrete topological group G be algebraically gen-
erated by a nowhere dense subset ?
Thank you for any help .
Is there somone help me to show that if this problem have positive Answer :
Problem :Can every non-discrete topological group G be algebraically gen-
erated by a nowhere dense subset ?
Thank you for any help .
According to this paper on open problems in topological algebra, this is an open problem (it's listed as Problem 9 in particular).
Problem 9 (Protasov). Can every topological group be algebraically generated by a nowhere dense subset?
Let us mention that each countable topological group is algebraically generated by some closed discrete subset (see reference in [13]) while every left topological group is algebraically generated by some subset with empty interior [13].
[13] in particular is from 2001.