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A surface is a generalization of a plane which needs not be flat, that is, the curvature is not necessarily zero. This is analogous to a curve generalizing a straight line

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Let K be a compact set in a surface, U component of S-K, K'=S-U. K has finitely many compone... [closed]

Let $S$ be a compact connected surface. Let $K$ be a compact subset of $S$ and suppose that $K$ has a finite number of connected components. Let $U$ be a connected component of $S \setminus K$ and con …
Fernando Oliveira's user avatar