reserve X for TopSpace;
reserve C for Subset of X;
reserve A, B for Subset of X;

theorem Th8:
  A is condensed & Cl Int A c= Int Cl A implies A is open & A is closed
proof
  assume that
A1: A is condensed and
A2: Cl Int A c= Int Cl A;
A3: A is closed_condensed by A1,A2,Th7;
  A is open_condensed by A1,A2,Th7;
  hence thesis by A3,TOPS_1:66,67;
end;
