reserve x,y for set;
reserve s,r for Real;
reserve r1,r2 for Real;
reserve n for Nat;
reserve p,q,q1,q2 for Point of TOP-REAL 2;

theorem Th2:
  for TX being non empty TopSpace, P being Subset of TX,
  A being Subset of TX|P, B being Subset of TX
  st B is closed & A=B/\P holds A is closed
proof
  let TX be non empty TopSpace,P be Subset of TX, A be Subset of TX|P,
  B be Subset of TX;
  assume that
A1: B is closed and
A2: A=B/\P;
  [#](TX|P)=P by PRE_TOPC:def 5;
  hence thesis by A1,A2,PRE_TOPC:13;
end;
