Let F: X x Y -> Z. We say that F is continuous in each variable separately if for each y(adsbygoogle = window.adsbygoogle || []).push({}); _{0}in Y, the map h: X-> Z defined by h(X)= F( x x y_{0}) is continuous, and for each x_{0}in X, the map k: Y-> Z defined by k(y) =F(x_{0}x y) is continuous. Show that if F is continuous, then F is continuous in each variable separately.

I'm not sure how to do this....

if you guys would help me out that would be amazing!

Thank You

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# Topology continuity

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