reserve Y for TopStruct;
reserve X for non empty TopSpace;
reserve X for almost_discrete non empty TopSpace;
reserve X,Y for non empty TopSpace;
reserve X for discrete non empty TopSpace,
  X0 for non empty SubSpace of X;

theorem Th66:
  ex r being continuous Function of X,X0 st r is being_a_retraction
proof
  reconsider A = the carrier of X0 as Subset of X by TSEP_1:1;
  defpred X[set,set] means $1 in A implies $2 = $1;
A1: for x being Point of X ex a being Point of X0 st X[x,a];
  consider r being Function of X,X0 such that
A2: for x being Point of X holds X[x,r.x] from FUNCT_2:sch 3(A1);
  reconsider r as continuous Function of X,X0 by Th62;
  take r;
  thus thesis by A2,BORSUK_1:def 16;
end;
