Re: product topology

On 22-10-2007 14:41, sanchopancho80@xxxxxx wrote:

does anybody know a counterexample for the following statement?

Let X, Y and Z be topological spaces and F:XxY --> Z be a mapping,
such that F(x,-):Y --> Z and F(-,y):X --> Z are continuous for every x
in X and every y in Y. Then F is continuous.

Consider f:R^2 ---> R defined by f(0,0) = 0 and f(x,y) = x.y/(x^2 + y^2)
otherwise. It is discontinuous at (0,0).

Best regards,

Jose Carlos Santos
.

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