The former message must be read this way. (Modifications marked by two 
stars.)

I think you should adapt your *EEhil* (and RR^) definition so that the 
> topology and uniform structure are generated from the distance. Currently 
> and unless I'm mistaken (the definitions are sometimes a little confusing) 
> I think they are independent. It will allow to speak of EEhil as a Hilbert 
> space with a standard norm defined from the inner product, a standard 
> distance defined from the norm, a uniform structure defined from the 
> distance, and a standard topology defined from the uniform structure.
>
>

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