
theorem
  for V being RealUnitarySpace, M being Subset of TopUnitSpace V st M =
  [#]V holds M is open & M is closed
proof
  let V be RealUnitarySpace;
  let M be Subset of TopUnitSpace V;
A1: [#](TopUnitSpace V) = the carrier of (TopStruct(#the carrier of V,
    Family_open_set(V)#));
  assume M = [#]V;
  hence thesis by A1;
end;
