$t$-adic topology (on $\mathbb F_p(1/t)$) Recently I found this interesting discussion about algebraically closed fields of positive characteristic. In the answer marked as the top answer, I read about the $t$-adic topology. The $t$-adic topology is unfamiliar to me and I could not seem to find anything via google. I do know something about the $p$-adic topology though (cf this ). So my question is if the $t$-adic topology is defined in the same way as the $p$-adic topology just with a $t$ instead of a prime numbre. I hope you guys can help me.

Yes, just the same. You can easily check what the completion of $k(1/t)=k(t)$ is. Best to look first at the $(t)$-adic completion of the ring $k[t]$: this is the ring $k[[t]]$ of formal power series in $t$ over $k$. Then the associated complete ring is $k((t))$, the (finite-tailed) formal Laurent series over $k$. When $k$ is finite, your field is a member of the small but tremendously interesting class of locally compact but not discrete topological fields.