Talk:Combination Theorem for Cauchy Sequences/Product Rule

I was hoping to use this theorem and the theorem Combination Theorem for Cauchy Sequences/Sum Rule to establish that the Cauchy Sequences of a valued field are a commutative ring with pointwise addition and multiplication, and thereby establish that the Completion of Valued Field was a field. But I no longer think that this will do it as the theorems are about normed vector spaces and not normed division rings. What do others think? --Leigh.Samphier (talk) 07:07, 29 August 2018 (EDT)


 * If the normed etc. etc. can all be proved to be metric spaces, then the job is done because the results have already been proved for metric spaces. --prime mover (talk) 09:42, 29 August 2018 (EDT)