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==Counterexamples in dimension one==
The theorem does not hold when {{math|''n'' {{=}} 1}}. To see this, it suffices to consider the function {{math|''f''(''z'') {{=}} ''z''<sup>−1</sup>}}, which is clearly holomorphic in {{math|'''C''' \ {0},}} but cannot be continued as a holomorphic function on the whole {{math|'''C'''}}. Therefore, the Hartogs's phenomenon is an elementary phenomenon that highlights the difference between the theory of functions of one and several complex variables.
== Notes ==
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