most recent 30 from http://mathoverflow.net 2013-05-20T01:20:49Z http://mathoverflow.net/feeds/user/18462 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/77892/a-doubtful-condition-for-continuity bulai 2011-10-12T04:03:33Z 2011-10-12T04:30:01Z

<p>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. </p>