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  "body": "\n## Summary\n\nA topological ring is a [[ring|0B1261B5ED]] with a [[topology|0CQHFPGJ45]] in which addition, negation and multiplication are continuous.\nIt lets one speak of limits, convergent series and completions inside a ring.\nThe real and complex numbers, the [[$p$-adic numbers|BT6T702C28]] and rings of formal power series with the $(x)$-adic topology are standard examples.\nA [[topological field|D7YQW9RG24]] is a topological ring that is a field and in which inversion is also continuous on nonzero elements.\n\n## Explanations\n\n### L1 human\n\nA topological ring is a ring where it makes sense to say that elements are \"close\" to each other, and the ring operations respect closeness.\nIf $a$ is close to $a'$ and $b$ is close to $b'$, then $a + b$ is close to $a' + b'$ and $ab$ is close to $a'b'$.\nThe real numbers with the usual distance are the basic example.\nIn the integers with the $p$-adic topology, a number is close to $0$ when it is divisible by a high power of $p$.\n",
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