We know from functional analysis that if a linear map is compact, then it is continuous. Now I want to find a nonlinear compact map that is not continous. Can someone help me with an idea?
Thanks!
2026-03-25 17:38:45.1774460325
Example of a nonlinear compact operator that is not continuous
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$F:\mathbb R\to\mathbb R$ with $F(x) = \arctan(x)$ for $x<0$ and $F(x) = \arctan(x)+1$ for $x\ge 0$.