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 .



Can every non-discrete topological group G be algebraically generated by a nowhere dense subset?
According to [this paper on open problems in topological algebra](http://www.researchgate.net/profile/Taras_Banakh/publication/221662575_Some_Open_Problems_in_Topological_Algebra/links/0fcfd50b52c10ec422000000.pdf), 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]](http://link.springer.com/article/10.1023%2FB%3AMATN.0000043466.45064.97)) while every left topological group is
>  algebraically generated by some subset with empty interior [[13]](http://link.springer.com/article/10.1023%2FB%3AMATN.0000043466.45064.97).
> 
> 
> 


[13] in particular is from 2001.


