Posted by J. Holmer on November 11, 2007, 7:15 pm, in reply to "2d, 23"
Board Administrator
2d: Yes.
23: An example of a separately continuous function that is not continuous is:
f(x,y) = xy/(x^2+y^2) if (x,y) \neq 0 and
f(0,0) = 0
If x=0, then f(0,y) = 0 and thus continuous
If y=0, then f(x,0) = 0 and thus continuous
If x=y, then f(x,y) = 1/2, and sending x\to 0, we see that it is not continuous.
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