Next | Topology of Data Types | 10 |
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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