Weierstra Theorem. Tests x<0, x=0, x>0: undecidable. Continuity for Functions. ?x?X. ?e>0. ??>0. ?x\'?X:. d(x,x\')<? ?? d(y,y\')<e. where y=f(x), y\'=f(x\'). uniform. continuity of f:X?Y. X,Y metric spaces,. Facts: a) X compact, f continuous ?? uniformly sob) f computable ? continuousc)
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