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A surface is a two-dimensional topological manifold. The term can also be used to describe a smooth surface, depending on the context.

10 votes

If $A$ is the ring of continuous functions on a genus $g$ surface, can the genus of $X$ be s...

The torus has two functions $f$ and $g$ which are (1) relatively prime, (2) each have two square roots, and (3) whose product has $4$ square roots. For instance take two functions which vanish on disj …
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