Spooky geometry V

The complement of an algebraic set in A^n(\Bbb{C}) is path-connected.

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Spooky geometry V

One thought on “Spooky geometry V

  1. Let x,y be points in the complement of an algebraic set X\subseteq A^n(\Bbb{C}). The (complex!) line joining x and y, which is homeomorphic to \Bbb{C}, intersects X in at most finitely many points, so there is a path connecting x and y inside it that does not intersect X.

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