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f is continuous if f^-1(G) is open whenever G is

That is, if f^-1(G) is semidecidable whenever G is semidecidable

Say f is discontinuous

Then there is a semidecidable G for which f^-1(G) is not semidecidable

But here's an algorithm for semideciding f^-1(G):

given semidecidable G, and x, is x \in f^{-1}(G)?
if G(f(x)): then

YES

else

NO

So are there are no discontinuous functions??

continued...

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