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The tag has the following description:

For questions about Riemann surfaces, that is compact analytic manifolds of (complex) dimension 1, and related topics.

The usual definition is that they be analytic manifolds with complex dimension $1$, so why are they defined as being compact here?

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  • $\begingroup$ Interestingly, tag-excerpt mentions compactness, but the body of the tag-wiki does not. $\endgroup$ Apr 18, 2016 at 4:42
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    $\begingroup$ I venture the guess that the intention was to write "complex" and the muscle memory chose the wrong continuation to autocomplete. $\endgroup$ Apr 18, 2016 at 8:47

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I don't expect that we shall ever know why the word "compact" appeared in the excerpt. It's almost exactly five years since the creation of the tag wiki excerpt (the tag wiki itself was however only created last year), and even if it was deliberate, I doubt the creator would still know the reason.

Anyway, I went ahead and edited the excerpt.

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