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File:Continuous Functions – Non-continuous 2d-example (view 1).svg

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English: The function f: R²→R, f(x,y)=f(0,0):=0 for x=y=0 and f(x,y):=xy/(x²+y²) otherwise, is not continuous in (0,0), despite f_y: R→R, f_y(x):=f(x,y) for any fixed y is continuous just as is f_x: R→R, f_x(y):=f(x,y) for any fixed x.
Deutsch: Die Funktion f: R²→R, f(x,y)=f(0,0):=0 für x=y=0 und f(x,y):=xy/(x²+y²) andernfalls, ist nicht stetig im Punkt (0,0), obwohl für beliebiges festes y f_y: R→R, f_y(x):=f(x,y) stetig ist wie auch für beliebiges festes x f_x: R→R, f_x(y):=f(x,y).
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