theorem Th22:
  weight TM c= iC iff density TM c= iC
proof
  consider A be Subset of TM such that
A1: A is dense and
A2: density TM=card A by TOPGEN_1:def 12;
  hereby
    assume weight TM c=iC;
    then for F be Subset-Family of TM st F is open & not{} in F & for A,B be
Subset of TM st A in F & B in F & A<>B holds A misses B holds card F c=iC by
Th21;
    hence density TM c=iC by Lm6;
  end;
A3: weight TM c=omega*`card A by A1,Th17;
  assume density TM c=iC;
  then omega*`card A c=omega*`iC by A2,CARD_2:90;
  then weight TM c=omega*`iC by A3;
  hence thesis by Lm5;
end;
