Is it true that [tex]f[/tex] is a continuous function from [tex]A \times B[/tex] to [tex]C[/tex](adsbygoogle = window.adsbygoogle || []).push({});

(A, B, C are topological spaces)

if and only if [tex]f_{a}: \{a\}\times B \longrightarrow C[/tex] and [tex]f_{b}: A\times \{b\} \longrightarrow C[/tex] are continuous for all [tex]a\in A, b\in B[/tex] ?

[tex]f_a(b) = f_b(a) = f(a,b)[/tex]

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# Continuous function

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