Next Topology of Data Types 10

# Continuity

• 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??

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