sentences:  In homotopy theory, Sullivan put forward the radical concept that spaces could directly be "localised", a procedure hitherto applied to the algebraic constructs made from them.He founded (along with Daniel Quillen) rational homotopy theory.The Sullivan conjecture, proved in its original form by Haynes Miller, states that the classifying space "BG" of a finite group "G" is sufficiently different from any finite CW complex "X", that it maps to such an "X" only 'with difficulty'; in a more formal statement, the space of all mappings "BG" to "X", as pointed spaces and given the compact-open topology, is weakly contractible.