Extensions of maps to the projective plane

It is proved that for a 3-dimensional compact metrizable space X the infinite real projective space is an absolute extensor of X if and only if the real projective plane is an absolute extensor of X.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-69.abs.htm