The Frankl-Peng-Rodl-Talbot Question on Turan Density Intervals
Frankl, Peng, Rodl and Talbot asked in 2007 whether the set of Turan densities of families of $r$-graphs contains intervals. It does: for every $r \ge 3$ the set contains non-degenerate intervals, including one of the form $[1-\delta_r, 1]$.