The ring $R$ is complete both for the $\langle X \rangle$-adic topology and for the $\langle t, X \rangle$-adic topology. So it depends on what you want to study about $R$.
– Leo AlonsoApr 29 '13 at 14:20

The question is subtler than it appears, depending on the topology you choose its formal spectrum is completely different.
– Leo AlonsoApr 29 '13 at 14:27

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I think there is no "natural" topology, as Leo says.
– Filippo Alberto EdoardoApr 29 '13 at 15:39