One-sided Heegaard splittings of RP^3
  Using basic properties of one-sided Heegaard splittings, a direct proof that geometrically compressible one-sided splittings of RP^3 are stabilised is given. The argument is modelled on that used by Waldhausen to show that two-sided splittings of S^3 are standard. 
Loretta Bartolini, J Hyam Rubinstein