1

At the beginning of my study in analysis I learned something about convergence of sequences for example, metric spaces and so forth... Most of the time we considered metric spaces $(\mathbb{K}, d), \mathbb{K} \in \{\mathbb{R},\mathbb{C} \}$ with a suitable metric d or sometimes function spaces with a suitable metric.I am embarrassed by my question a littlebit. I never heard something about if $\mathbb{K}$ is a finite field, for example $\mathbb{F_7}$. Does it make sense to accredit such a finite field with a metric and talk about concepts like convergence of sequences for example? If it is possible, can you show me an example or give me a reference? Best, RedRose

RedRose
  • 81
  • You may want to read about $;p$-adic numbers... – DonAntonio Mar 26 '14 at 17:56
  • 1
    This isn't an answer to your question, but you should observe that any finite set equipped with any metric whatever automatically acquires the discrete topology, and thus convergent sequences are exactly those that are eventually constant. I would be somewhat surprised if anything interesting could be made of this. – MJD Mar 26 '14 at 18:36
  • oh, this are very helpful remarks for me, thank you! – RedRose Mar 26 '14 at 18:48

0 Answers0