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Essentially, I'm trying to find an example of a function that is continuous but not uniformly continuous on $\text{GL}(2,\Bbb{C})$. I'm aware that this group is isomorphic (up to constant multiples) to the Möbius transformations. So I'm having a go at developing some geometric intuition there. However, as my prior inquiries indicate, my epsilon-delta skills are lacking. Hence, I find these sorts of examples tough to fabricate.

Edit: Norm is the boring Euclidean one on $\Bbb{C}^4$.

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    I suggest that you try to concoct a few more examples and post them as an answer. Then ping me and I'll have a look.2012-05-03

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