f:R->R satisfies that the image of every open interval is an open interval. Does this imply that f is continuous on R? ALTERNATIVE STATEMENT: f:(a,b)->R(where (a,b) is obviously in R) satisfies: "(c,d) is a subset of (a,b) implies that f((c,d)) is an open interval." Does this imply that f is continuous on R? N.B.:The open intervals mentioned above are all finite in the sense that they are of the form (x,y),where x,y are real numbers.
closed as too localized by Will Jagy, Gjergji Zaimi, Ricky Demer, Alex Bartel, Andres Caicedo Oct 12 2011 at 4:50