Picard theorem

In complex analysis, Picard's theorem (named after Émile Picard) tells about the range of a function. In brief, they state that a flat function can't transition into a non-flat function: if a function is zero at two neighboring points (i.e. flat), then it must be zero everywhere. Alternatively: sufficiently near to a zero, a function must have non-zero values.

Category:Mathematical theorems
Category:Complex analysis