 Solution

ID: past-exam-of-the-metric-spaces-and-complex-analysis-course-of-the-university-of-oxford/2023/4/a/ii/solution

a

F

on a full disc

B (a, r)

agreeing with

f

away from

a

. Equivalently,

z \to a lim f (z) = L \in C, F (a) = L .

The Riemann removable singularity theorem also characterizes this by boundedness of

f

on a sufficiently small punctured disc. A preassigned incorrect value at

a

is replaced by

L

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