
theorem
  for T being non empty TopSpace
  for x being Element of InclPoset the topology of T st x = the carrier of T
  holds x is compact iff T is compact
proof
  let T be non empty TopSpace;
  let x be Element of InclPoset the topology of T;
  assume
A1: x = the carrier of T;
  T is compact iff [#]T is compact;
  hence thesis by A1,Th36;
end;
