Question
The Casorati-Weierstrass theorem is a result of this field of analysis concerning essential singularities of holomorphic functions. For 10 points each:
[10e] Name this field of analysis, contrasted with ‘real analysis’ that concerns functions whose variables have both real and imaginary parts.
ANSWER: complex analysis
[10m] The Casorati-Weierstrass theorem states that the image of a punctured neighbourhood of an essential singularity has this property in the complex numbers. The rational numbers have this property in the reals since there is a rational between any two real numbers.
ANSWER: dense [accept word forms]
[10h] This mathematician’s “great” theorem improves on the Casorati-Weierstrass theorem by showing that in fact, the function takes every complex value on the punctured neighbourhood, except possibly one.
ANSWER: Émile Picard [accept Picard’s (great) theorem]
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