How can I show that [tex]F:X\times I\to I[/tex] given by [tex]F(x,t)=(1-t)f(x)+tg(x)[/tex] is continuous, given that [tex]f:X\to I[/tex] and [tex]g:X\to I[/tex] are continuous (here I is the unit interval [0,1]). It seems that F is continuous, but I want to show that explicitly. Any help appreciated! X is any topological space.(adsbygoogle = window.adsbygoogle || []).push({});

(I wasn't sure what section to put this in - sorry!)

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# X is any topological space

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