reserve X for TopStruct,
  A for Subset of X;
reserve X for TopSpace,
  A,B for Subset of X;
reserve X for non empty TopSpace,
  A for Subset of X;

theorem Th10:
  A is boundary implies A <> the carrier of X
proof
  assume
A1: Int A = {};
  assume A = the carrier of X;
  then A = [#]X;
  hence contradiction by A1,TOPS_1:15;
end;
