
theorem Th8:
  for T being TopSpace st T is empty holds the topology of T = {{}}
proof
  let T1 be TopSpace;
  assume T1 is empty;
  then
A1: the carrier of T1 = {};
  then {} in the topology of T1 by PRE_TOPC:def 1;
  hence thesis by A1,ZFMISC_1:1,33;
end;
