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Topology continuity

  1. Feb 24, 2009 #1
    Let F: X x Y -> Z. We say that F is continuous in each variable separately if for each y0 in Y, the map h: X-> Z defined by h(X)= F( x x y0) is continuous, and for each x0 in X, the map k: Y-> Z defined by k(y) =F(x0 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
  2. jcsd
  3. Feb 24, 2009 #2


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    What is the definition of F being continuous?
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